First, PMC does not sell any light armor piercing ammo (at least according to the legal definition). AP ammo is prohibited by law generally. What you may be referring to is the 62gr ammo with a 4.7gr steel penetrator in the nose so that it can penetrate 10ga steel at 600yds (the older 55gr M193 cannot do that reliably). The LAP designation is more about marketing than fact.
Lake City is a govvernment owned arsenal. Private manufacturers bid to run the plant. Currently ATK/Federal has the contract.
SS109 is the Fabrique Nationale designation for the 5.56mm cartridge they developed for the M249 SAW. It is a 62gr bullet with a 4.7gr penetrator and meets the 600yd test described above. This was adopted by NATO as the standardized 5.56x45 round for NATO.
M855 is the U. S. designation for their version of SS109 ammo. Although SS109 ammo is "standardized", every country has their own variant. For example, the Australian SS109 isn't ideal for M16s and the U.S. M855 isn't great for the Australian service rifle (an AUG variant). Federal sells XM855 on the civilian market using the same components it uses to make M855; but these are not subjected to the same quality control as M855.
M855 was replaced in military service by M855A1, which is a lead free ammo that uses a copper bullet and no penetrator.
And to answer your question, I prefer Lake City/Federal assuming similar pricing.