Well, according to Canbat, there are two main reasons: charging and discharging. When charging a lithium battery, you require a higher voltage compared to charging a lead acid battery. If you use a lithium charger, you will over-charge the lead acid battery and damage it. If you use an AGM charger, you won’t be able to fully recharge the lithium battery because of the lower voltage AGM chargers output. Likewise, when discharging an AGM battery, you’re only technically supposed to be discharging up to 50% for the sake of longevity, but you can of course discharge a lot more with lithium. If you have both batteries connected to discharged together and your DOD cut-off is set at 50%, you won’t be able to utilize the true deep cycling capabilities of lithium. It won’t even be possible to discharge both batteries to 50%. This is because AGM state of charge is calculated based on the battery’s voltage while lithium state of charge is calculated based on algorithm which considers both the voltage and the current. This is why battery monitors, such as those made by Victron, require you to specify the type of battery you’re using. Canbat also mentioned other reasons, such the fact that lithium has a very high efficiency ratio of 99% where lead acid efficiency is about 70% and they went on. Nevertheless, the main two reasons is because AGM and lithium recharge and discharge differently.
Actually, in the video he connected LiFePO4 and FLA in parallel.
But let's discuss particular situation ...
First you claim, "a LiFePo4
requires a higher voltage than an AGM"
Explain why you can't use 14.4 volts for the LiFePO4 battery?
That looks like the exact same voltage for AGM at 70°F.
You think 14.4 volts is too low for LiFePO4 battery - you are joking, right?
You need to specify the voltage you think is "required" for LiFePo4, because you have not.
Secondly you claim, "you won't be able to utilize the true deep cycle cycles of lithium".
Actually, we can and will get 80+% DOD from the LiFePO4 battery.
The Low Voltage Drop-Out voltage will be that of the AGM.
And the TOTAL amp-hours is the SUM of both battery banks.
You need to do some actual research regarding this issue.
Third you claim, "lithium has a high efficiency of 99% where lead acid efficiency is about 70%"
So what?
This causes no problems.
Nevertheless, you still have not given a single valid reason WHY this cannot be done.