LiFeP04 battery is close to 100% SOC at 13.6-13.7v Lithium chargers do charge at a higher voltage but that is more of a function of charging faster than being fully charged. If you look at the charge curve for LiFePO4 you are talking less than 1 or 2 % above 13.7v A stock Progressive Dynamics converter charger has a 13.6v output.
In short your stock converter charger will charge a lithium battery. Pretty much all the battery manufacturers include this fact in their literature. It will take longer than a LiFePO4 charger as it tapers current through stages.
Have a look at the charge curve and you will see that 13.6v is essentially 100%
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