The LiFePO4 aka LiFe type of Lithium-Ion battery really needs a charger that does not drop below 14V (like the bike's alternator provides) or it will not achieve full charge.
http://www.powerstream.com/LLLF.htm - quote -
A LiFePO4 battery can be safely overcharged to 4.2 volts per cell, but higher voltages will start to break down the organic electrolytes. Nevertheless, it is common to charge a 12 volt a 4-cell series pack with a lead acid battery charger. The maximum voltage of these chargers, whether AC powered, or using a car's alternator, is 14.4 volts. This works fine, but lead acid chargers will lower their voltage to 13.8 volts for the float charge, and so will usually terminate before the LiFe pack is at 100%.
For this reason a special LiFe charger is required to reliably get to 100% capacity.
The Lithium-Ion really require a two-step charging process, step 1 constant current, step 2 constant voltage.
Four cells of nominal 3.2V gives 12.8V but note full charge voltage is nominal 3.7V per cell hence 14.8V on full charge. Past pro experience by our team found some 12VDC electronic equipment under test did not appreciate this and inconveniently blew up. Light bulbs will draw more current on this voltage and may blow or have their life reduced. The lead-acid has six cells of 2.1V each providing 12.6VDC or less.