I just fixed a very similar problem...
1976 CB550F, new Rick's Rect/Reg, and 3 1/2 year old Ballistic EVO2-8 Lithium battery I robbed from my dirtbike(KTM w/ electric & kickstart).
Battery was at the bare minimum resting charge voltage of 13.2v. Battery Tender Plus said it was charged. Turn on the key battery dropped to 6v and headlight dimmed to nothing. Kick it and it fired up, ~11v at idle and ~15.5v at 3K rpm...WTF?
Rather than asking here and raising angst of Lithium haters I determined it had to be the battery.
Got a Scorpion LiFePO to try out, installed it and everything perfect once again...all voltage at or near specs.
Sounds to me like you have the same problem.
Cheers,
Kenzo