<PAGE>   1
                                                                      EXHIBIT 24

                               POWER OF ATTORNEY


KNOW ALL MEN BY THESE PRESENTS, that the undersigned Director of LYNCH
CORPORATION, an Indiana corporation, hereby appoints ROBERT E. DOLAN and ROBERT
A. HURWICH true and lawful attorneys-in-fact and agents, and each of them (with
full power to act without the other) his true and lawful attorney-in-fact and
agent, with full power of substitution and resubstitution, for him and in his
name, place and stead, in any and all capacities, to sign, execute, deliver and
file with the Securities and Exchange Commission the Annual Report on Form 10-K
of Lynch Corporation for the fiscal year ended December 31, 1997, including any
and all amendments thereto, granting unto said attorneys and agents, and each
of them, full power to do and perform every act and thing requisite, necessary
or desirable to be done in connection therewith, as fully to all intents and
purposes as he might or could do in person, hereby ratifying and confirming all
that said attorneys-in-fact and agents, or any of them, or their or his
substitutes or substitute, may lawfully do or cause to be done by virtue
hereof, and hereby revoking all prior appointments by him, if any, of
attorneys-in-fact and agents to sign and file the above-described document,
including any and all amendments thereto.

IN WITNESS WHEREOF. the undersigned has hereunto set his hand and seal on the
date set forth below.


DATE: March 17, 1998                  s/ David C. Mitchell     (L.S.)
                                      -------------------------
                                      David C. Mitchell


s/ Carole L. Rau
-----------------------------
    Notary Public
<PAGE>   2

                               POWER OF ATTORNEY


KNOW ALL MEN BY THESE PRESENTS, that the undersigned Director of LYNCH
CORPORATION, an Indiana corporation, hereby appoints ROBERT E. DOLAN and ROBERT
A. HURWICH true and lawful attorneys-in-fact and agents, and each of them (with
full power to act without the other) his true and lawful attorney-in-fact and
agent, with full power of substitution and resubstitution, for him and in his
name, place and stead, in any and all capacities, to sign, execute, deliver and
file with the Securities and Exchange Commission the Annual Report on Form 10-K
of Lynch Corporation for the fiscal year ended December 31, 1997, including any
and all amendments thereto, granting unto said attorneys and agents, and each
of them, full power to do and perform every act and thing requisite, necessary
or desirable to be done in connection therewith, as fully to all intents and
purposes as he might or could do in person, hereby ratifying and confirming all
that said attorneys-in-fact and agents, or any of them, or their or his
substitutes or substitute, may lawfully do or cause to be done by virtue
hereof, and hereby revoking all prior appointments by him, if any, of
attorneys-in-fact and agents to sign and file the above-described document,
including any and all amendments thereto.

IN WITNESS WHEREOF. the undersigned has hereunto set his hand and seal on the
date set forth below.


DATE: March 17, 1998                  s/ E. Val Cerutti        (L.S.)
                                      -------------------------
                                      E. Val Cerutti


 s/ Carole L. Rau
---------------------------
    Notary Public
<PAGE>   3

                               POWER OF ATTORNEY


KNOW ALL MEN BY THESE PRESENTS, that the undersigned Director of LYNCH
CORPORATION, an Indiana corporation, hereby appoints ROBERT E. DOLAN and ROBERT
A. HURWICH true and lawful attorneys-in-fact and agents, and each of them (with
full power to act without the other) his true and lawful attorney-in-fact and
agent, with full power of substitution and resubstitution, for him and in his
name, place and stead, in any and all capacities, to sign, execute, deliver and
file with the Securities and Exchange Commission the Annual Report on Form 10-K
of Lynch Corporation for the fiscal year ended December 31, 1997, including any
and all amendments thereto, granting unto said attorneys and agents, and each
of them, full power to do and perform every act and thing requisite, necessary
or desirable to be done in connection therewith, as fully to all intents and
purposes as he might or could do in person, hereby ratifying and confirming all
that said attorneys-in-fact and agents, or any of them, or their or his
substitutes or substitute, may lawfully do or cause to be done by virtue
hereof, and hereby revoking all prior appointments by him, if any, of
attorneys-in-fact and agents to sign and file the above-described document,
including any and all amendments thereto.

IN WITNESS WHEREOF. the undersigned has hereunto set his hand and seal on the
date set forth below.


DATE: March 17, 1998                  s/ Paul J. Evanson       (L.S.)
                                      -------------------------
                                      Paul J. Evanson


 s/ Elsa M. Akin
---------------------------
    Notary Public
<PAGE>   4

                               POWER OF ATTORNEY


KNOW ALL MEN BY THESE PRESENTS, that the undersigned Director of LYNCH
CORPORATION, an Indiana corporation, hereby appoints ROBERT E. DOLAN and ROBERT
A. HURWICH true and lawful attorneys-in-fact and agents, and each of them (with
full power to act without the other) his true and lawful attorney-in-fact and
agent, with full power of substitution and resubstitution, for him and in his
name, place and stead, in any and all capacities, to sign, execute, deliver and
file with the Securities and Exchange Commission the Annual Report on Form 10-K
of Lynch Corporation for the fiscal year ended December 31, 1997, including any
and all amendments thereto, granting unto said attorneys and agents, and each
of them, full power to do and perform every act and thing requisite, necessary
or desirable to be done in connection therewith, as fully to all intents and
purposes as he might or could do in person, hereby ratifying and confirming all
that said attorneys-in-fact and agents, or any of them, or their or his
substitutes or substitute, may lawfully do or cause to be done by virtue
hereof, and hereby revoking all prior appointments by him, if any, of
attorneys-in-fact and agents to sign and file the above-described document,
including any and all amendments thereto.

IN WITNESS WHEREOF. the undersigned has hereunto set his hand and seal on the
date set forth below.


DATE: March 17, 1998                  s/ Salvatore Muoio       (L.S.)
                                      -------------------------
                                      Salvatore Muoio


  s/ Carole L. Rau
--------------------------
    Notary Public
<PAGE>   5

                               POWER OF ATTORNEY


KNOW ALL MEN BY THESE PRESENTS, that the undersigned Director of LYNCH
CORPORATION, an Indiana corporation, hereby appoints ROBERT E. DOLAN and ROBERT
A. HURWICH true and lawful attorneys-in-fact and agents, and each of them (with
full power to act without the other) his true and lawful attorney-in-fact and
agent, with full power of substitution and resubstitution, for him and in his
name, place and stead, in any and all capacities, to sign, execute, deliver and
file with the Securities and Exchange Commission the Annual Report on Form 10-K
of Lynch Corporation for the fiscal year ended December 31, 1997, including any
and all amendments thereto, granting unto said attorneys and agents, and each
of them, full power to do and perform every act and thing requisite, necessary
or desirable to be done in connection therewith, as fully to all intents and
purposes as he might or could do in person, hereby ratifying and confirming all
that said attorneys-in-fact and agents, or any of them, or their or his
substitutes or substitute, may lawfully do or cause to be done by virtue
hereof, and hereby revoking all prior appointments by him, if any, of
attorneys-in-fact and agents to sign and file the above-described document,
including any and all amendments thereto.

IN WITNESS WHEREOF. the undersigned has hereunto set his hand and seal on the
date set forth below.


DATE: March 17, 1998                  s/ Ralph R. Papitto       (L.S.)
                                      --------------------------
                                      Ralph R. Papitto


    s/ Carole L. Rau
----------------------------
    Notary Public
<PAGE>   6

                               POWER OF ATTORNEY


KNOW ALL MEN BY THESE PRESENTS, that the undersigned Director of LYNCH
CORPORATION, an Indiana corporation, hereby appoints ROBERT E. DOLAN and ROBERT
A. HURWICH true and lawful attorneys-in-fact and agents, and each of them (with
full power to act without the other) his true and lawful attorney-in-fact and
agent, with full power of substitution and resubstitution, for him and in his
name, place and stead, in any and all capacities, to sign, execute, deliver and
file with the Securities and Exchange Commission the Annual Report on Form 10-K
of Lynch Corporation for the fiscal year ended December 31, 1997, including any
and all amendments thereto, granting unto said attorneys and agents, and each
of them, full power to do and perform every act and thing requisite, necessary
or desirable to be done in connection therewith, as fully to all intents and
purposes as he might or could do in person, hereby ratifying and confirming all
that said attorneys-in-fact and agents, or any of them, or their or his
substitutes or substitute, may lawfully do or cause to be done by virtue
hereof, and hereby revoking all prior appointments by him, if any, of
attorneys-in-fact and agents to sign and file the above-described document,
including any and all amendments thereto.

IN WITNESS WHEREOF. the undersigned has hereunto set his hand and seal on the
date set forth below.


DATE: March 17, 1998                  s/ John C. Ferrara       (L.S.)
                                      -------------------------
                                      John C. Ferrara


   s/ Carole L. Rau
--------------------------
    Notary Public
<PAGE>   7
                               POWER OF ATTORNEY

KNOW ALL MEN BY THESE PRESENTS, that the undersigned, Director, Chairman of the
Board and Chief Executive Officer (Principal Executive Officer), of LYNCH
CORPORATION, an Indiana corporation, hereby appoints ROBERT E. DOLAN and ROBERT
A. HURWICH true and lawful attorneys-in-fact and agents, and each of them (with
full power to act without the other) his true and lawful attorney-in-fact and
agent, with full power of substitution and resubstitution, for him and in his
name, place and stead, in any and all capacities (including Director, Chairman
of the Board and Chief Executive Officer (Principal Executive Officer)), to
sign, execute, deliver and file with the Securities and Exchange Commission the
Annual Report on Form 10-K of Lynch Corporation for the fiscal year ended
December 31, 1997, including any and all amendments thereto, granting unto said
attorneys and agents, and each of them, full power to do and perform every act
and thing requisite, necessary or desirable to be done in connection therewith,
as fully to all intents and purposes as he might or could do in person, hereby
ratifying and confirming all that said attorneys-in-fact and agents, or any of
them, or their or his substitutes or substitute, may lawfully do or cause to be
done by virtue hereof, and hereby revoking all prior appointments by him, if
any, of attorneys-in-fact and agents to sign and file the above-described
document, including any and all amendments thereto.

IN WITNESS WHEREOF. the undersigned has hereunto set his hand and seal on the
date set forth below.


DATE: March 17, 1998                      s/ Mario J. Gabelli         (L.S.)
                                          ----------------------------
                                          Mario J. Gabelli



     s/ Carole L. Rau
-------------------------
  Notary Public