Lock for a door of the rebated type, comprising - a containing box body (2;102), suitable for being housed in a cavity of said rebated door; - a latch (3; 3'; 3") that is movable, along an entrance direction (D I), between an extracted position and a retracted position in said box body (2; 102); - driving means (4; 104; 204) movable, by means of a control handle, along an opening direction (D A), which is transverse to said entrance direction (D I), to move said latch (3; 3'; 3") from said extracted position to said retracted position, - said driving means (4; 104; 204) being movable, by a key-locking-member, along a locking direction (D B) opposite said opening direction (D A), to reach a disengaged position (P D) in which said driving means (4; 104; 204) is not engageable by said control handle thus preventing the driving of said latch (3; 3'; 3"), - a bolt (6; 106) that is drivable by said key-locking-member to move from a non-operative position (P N), in which it is retracted into said box body (2;102), to an operative position (P O) protruding outside said box body (2;102), CHARACTERISED IN THAT said driving means is defined by a cursor element (4; 104; 204) on which are obtained: - a pushing-portion (9a; 10a) shaped for moving said latch (3; 3'; 3") to said retracted position when said cursor element (4; 104; 204) advances along said opening direction (D A), - an engaging lug, placed in an intermediate zone of said cursor element (4; 104; 204), arranged for coupling with a lever that is drivable by said control handle to move said cursor element (4; 104; 204) along said opening direction (D A), - an abutting zone, obtained at an end which is opposite with respect to said pushing-portion (9a; 10a), and shaped for interacting with said key-locking-member of said lock (1;101), said abutting zone having a portion (16; 16') shaped for receiving from said key-locking-member a pushing action to move said cursor element (4; 104; 204) along said locking direction (D B) to said disengaged position (P D) in which it is disengaged from said lever AND IN THAT on said cursor element (4; 104; 204) locking means (7A, 7B) is obtained shaped for locking said latch (3; 3'; 3") in said extracted position, preventing forced movement thereof from the outside to said retracted position, when said cursor element (4; 104; 204) is in said disengaged position (P D) in which it is disengaged from said control handle. - a containing box body (2;102), suitable for being housed in a cavity of said rebated door; - a latch (3; 3'; 3") that is movable, along an entrance direction (D I), between an extracted position and a retracted position in said box body (2; 102); - driving means (4; 104; 204) movable, by means of a control handle, along an opening direction (D A), which is transverse to said entrance direction (D I), to move said latch (3; 3'; 3") from said extracted position to said retracted position, - said driving means (4; 104; 204) being movable, by a key-locking-member, along a locking direction (D B) opposite said opening direction (D A), to reach a disengaged position (P D) in which said driving means (4; 104; 204) is not engageable by said control handle thus preventing the driving of said latch (3; 3'; 3"), - a bolt (6; 106) that is drivable by said key-locking-member to move from a non-operative position (P N), in which it is retracted into said box body (2;102), to an operative position (P O) protruding outside said box body (2;102), - a pushing-portion (9a; 10a) shaped for moving said latch (3; 3'; 3") to said retracted position when said cursor element (4; 104; 204) advances along said opening direction (D A), - an engaging lug, placed in an intermediate zone of said cursor element (4; 104; 204), arranged for coupling with a lever that is drivable by said control handle to move said cursor element (4; 104; 204) along said opening direction (D A), - an abutting zone, obtained at an end which is opposite with respect to said pushing-portion (9a; 10a), and shaped for interacting with said key-locking-member of said lock (1;101), said abutting zone having a portion (16; 16') shaped for receiving from said key-locking-member a pushing action to move said cursor element (4; 104; 204) along said locking direction (D B) to said disengaged position (P D) in which it is disengaged from said lever