Hi Pixel,

Negative LRT values close to 0 (say -0.01) can be ignored because they are within numerical tolerances, and basically say that the null model is the same as the alternative model.
If you wish to find SITES subject to episodic selection, we suggest you use the MEME method, but be aware that you can't reliably find both SITES and LINEAGES subject to episodic selection. From the MEME paper:

The ability of MEME, or similar substitution model-based methods, to accurately infer the identity of individual branches subject to diversifying selection at a given site seems unavoidably limited. Most of the information that such inference might be based on is limited to character substitutions along a single branch at a single site, i.e. one realization of the Markov substitution process. Selection along terminal branches in the context of negatively selected background can be detected more reliably than selection along interior branches among neutrally evolving background lineages. However, we caution that despite obvious interest in identifying specific branch-site combinations subject to diversifying selection, such inference is based on very limited data (the evolution of one codon along one branch), and cannot be recommended for purposes other than data exploration and result visualization. This observation could be codified as the “selection inference uncertainty principle” – one cannot simultaneously infer both the site and the branch subject to diversifying selection. In this manuscript, we describe how to infer the location of sites, pooling information over branches; previously [20] we have outlined a complementary approach to find selected branches by pooling information over sites.

Sergei