The 5th Lyrans on Gypsum are actually the 5th Lyran Guards, as per the 4th Succession War Atlas vol I, page 44 (same planet and rating).
The unit rosters from the House books should be more or less complete. If we revisit that era we'll research if there are omissions, units mentioned in TROs and other places that does not fit the rosters for that year. But until then, what is in the House books is considered to be complete.
Mercenaries is always a touchy subject, since various sources vary greatly in how many mercenaries there are in the Inner Sphere. Our current view is that we list notable units, and most units above a certain size (ie battalion and larger). But even that has pitfalls enough to say that a full list of mercenaries in any age/era has never been compiled (and never will).
With regards,
Øystein