If you adjust the absorb and float both to 12 volts (if they go that low) you should get the voltage you need, mppt controller can control the voltage better then pwm. Lower voltage means lower amps going into the battery.
But I wouldn't trust any charge controller to charge lithiums, except maybe the electrodacus controller which can monitor the balance status of the battery. Its the only true lithium charge controller, all the others just monitor overall voltage but not the balance voltage which is where the danger is.
Its very easy for the battery to go out of balance while charging, and even if the controller stopped at 12.6 volts, one row of batteries might be severely over voltaged. Myself I wouldn't risk it and have charged both the li-ion and the lifepo4 batteries.
If you want to control that the battery doesnt go over a particular voltage, you can do what I do which is to put an overvoltage relay that will disconnect the panel from the controller when the voltage reaches 12 volts, this is how I do it. It works everytime. But even this isn't good enough for me because what if the battery goes out of balance, to me its more of a deadman switch.
I notice that if I set my ecoworthy mppt to 12 volts, my li-ion (11.1 volt battery pack never got charged, it just trickle charged at 3 or 4 amps). My lifepo4 I had to raise the voltage to 15.5 volts to fast charge. You need higher voltages if you want to fast charge them. Lower voltages are much safer but I still wouldnt trust them unless the charger can monitor the balance voltage. The only time I saw my lifepo4 go under 12.9 volts was when it only had 30 percent power left, once it goes to 12.8 volts it will quickly go to empty.
When I want to fully charge my lithiums I have been using a 14 amp ISDT q6 balance charger, they use them in the RC world, it will hit the battery with maximun amps and make sure it don't go out of balance. My ecoworthy mppt, I only use it to slow charge my lithiums.
This controller is suppose to be lithium capable, and I tested it and it actually didnt stop the charge at 12.6 volts like it was suppose to. Thats why I would recommend a overvoltage relay on any lithium battery. Controller can fail or bms can fail.