What's wrong with my charging system?

I have a 1983 Honda CB550SC. A month or two ago I replaced the regulator/rectifier, and yesterday I replaced the stator. The output off the stator is ~12v AC at idle, and goes up to 15 at higher RPMs.

My battery is a lithium one by Deltran. I charged it over night on Monday (13.5v), and yesterday after replacing the alternator, went for a short ride to an appointment and back home, then was going to a friends house I got a mile away from home and it just shut down. I've learned to ride with a multimeter and it was down to 9.x v. I had someone jump me and left the thing at a friends place. So with my alternator obviously putting out a charge, what is wrong here? I'm at a total loss.

Another bit of info, not sure if it's relevant or not, is that my signals speed up with higher RPMs and slow down at idle.

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