Using the time-dependent theory, we calculate the random-laser emission spectra in a two-dimensional strongly disordered medium. The calculation results show that in low dimensional systems, such as thinfilm disordered media and planar waveguides, the larger the difference of the refractive indices between the scattering and background media, the smaller the lasing threshold. We also reveal the existence of multimode survival and mode competition. We experimentally obtain the emission spectra of a dye solution with Al particles doped at different pumping energies, and the experimental results agree well with the calculated ones.