LIME solves the molecular and atomic excitation and radiation transfer problem in a molecular gas and predicting emergent spectra. The code works in arbitrary three dimensional geometry using unstructured Delaunay latices for the transport of photons. Various physical models can be used as input, ranging from analytical descriptions over tabulated models to SPH simulations. To generate the Delaunay grid we sample the input model randomly, but weigh the sample probability with the molecular density and other parameters, and thereby we obtain an average grid point separation that scales with the local opacity. Slow convergence of opaque models becomes traceable; when convergence between the level populations, the radiation field, and the point separation has been obtained, the grid is ray-traced to produced images that can readily be compared to observations. LIME is particularly well suited for modeling of ALMA data because of the high dynamic range in scales that can be resolved using this type of grid, and can furthermore deal with overlapping lines of multiple molecular and atomic species.