With the aim of improving predictions on far-infrared (FIR) line emission from Giant Molecular Clouds (GMCs), we study the effects of photoevaporation (PE) produced by external farultraviolet (FUV) and ionizing (extreme-ultraviolet) radiation on GMC structure. We consider three different GMCs with mass in the range M-GMC = 10(3)-10(6)M(O). Our model includes (i) an observationally based inhomogeneous GMC density field, and (ii) its time evolution during the PE process. In the fiducial case (M-GMC approximate to 10(5)M(O)), the PE time (t(pe)) increases from 1 to 30 Myr for gasmetallicityZ = 0.05-1 Z(O)), respectively. Next, we compute the time-dependent luminosity of key FIR lines tracing the neutral and ionized gas layers of the GMCs, ([C II] at 158 mu m, [O III] at 88 mu m) as a function of G(0), and Z until complete PE at t(pe). We find that the specific [C II] luminosity is almost independent of the GMC model within the survival time of the cloud. Stronger FUV fluxes produce higher [C II] and [O III] luminosities, however, lasting for progressively shorter times. At Z = Z(O), the [CII] emission is maximized (LCII approximate to 10(4) L-O for the fiducial model) for t < 1Myr and logG(0) >= 3. Noticeably, and consistently with the recent detection by Inoue et al. of a galaxy at redshift z approximate to 7.2, for Z = 0.2Z(O), the [OIII] line might outshine [C II] emission by up to approximate to 1000 times. We conclude that the [OIII] line is a key diagnostic of low-metallicity interstellar medium, especially in galaxies with very young stellar populations.