I did not check the original literature but as far as I know Bonasa was first used for Bonasa umbellus (dating back to Stephens, 1819) while Tetrastes was invited by Keyserling & Blasius, JH, 1840. The split followed in most recent taxonomic lists between both genera is mainly based on Gutiérrez et al 2000 (http://wordpress.cfans.umn.edu/gutierrez/files/2013/03/cfans_content_378259.pdf) - at least this is true for the official German bird list/taxonomy (Bauer et al 2005). Therefore, Bonasa is restricted to umbellus while the plaearctic species form Tetrastes. Lyrurus and Tetrao are closely related and accepting both genera seems to be rather a matter of taste. If they are lumped Tetrao is the original Linnean name which has priority over Lyrurus Swainson, 1832.
I found one article on the web that might be interesting for you:
To clarify, most studies of the grouse (not just that of Gutiérrez et al 2000) indicate that the genus Bonasa (as traditionally circumscribed) is not monophyletic (Ellsworth et al. 1996, Dimcheff et al. 2000, 2002, Gutiérrez et al. 2000, Crowe et al. 2006). The split of Bonasa into two genera is therefore widely accepted and Hazel Grouse B. bonasia and Severtsov’s Grouse B. sewerzowi are now placed in Tetrastes.
On the other hand, recognition of Lyrurus for the two black grouse, i.e. a split of Tetrao into two genera, is possible but unnecessary. The black grouse and capercaillies are sister-taxa (Ellsworth et al. 1996, Dimcheff et al. 2000, Crowe et al. 2006) and studies that included all four species found that the two black grouse are sister to the two capercaillies (Gutiérrez et al. 2000, Lucchini et al. 2001, Dimcheff et al. 2002, Drovetski 2002). Keeping these species in a single genus seems the best option.
See the link below for a discussion of the arguments pro and con for recognising Lyrurus.
Article Taxonomic recommendations for British birds: Eighth report