  The production of axionlike particles (ALPs) with small masses in
ultraperipheral $Pb - p$ and $Pb - Pb$ collisions at the LHC is investigated.
The cross section and kinematical distributions associated to the diphoton
final state produced in the $\gamma \gamma \rightarrow a \rightarrow \gamma
\gamma$ subprocesses are estimated considering a realistic set of kinematical
cuts. A detailed analysis of the backgrounds is performed and the expected
sensitivity to the ALP production is derived. Our results demonstrate that a
future experimental analysis of the exclusive diphoton production for the
forward rapidities probed by the LHCb detector can improve the existing
exclusion limits on the ALP - photon coupling in the mass range 2 GeV $\le m_a
\le$ 5 GeV.
