Main things with Lithium are charging and discharge protection. The one you linked has a BMS which
should take care of all that for you. Basically, if you run a lithium battery flat you will likley kill it. A lithium battery will supply good voltage right till 15-20% charge (then the BMS will kick in) while an AGM will only give you good voltage till about 40% charge, for a good quality one. There
can be a risk of fire if lithium batteries are treated improperly.
If you have a lithium battery, you need either a built in BMS or a dedicated lithium charger, ideally one with cell monitoring. This is because Lithium batteries are made up of multiple 'cells' (much like the plates in a lead battery) which are 3.7v. The danger is each cell can be discharged/charged at a slightly different rate due to thermal gradients accross the battery, wiring, the quality of the packs etc. This means that while the
nominal pack voltage reads at say, 30% charge, you maye have one pack at 3.0V (over discharged, bad) and the rest at a normal level, averaging the voltage out. Cell monitoring checks the voltage of each single cell and can charge each cell individually to 'balance' the battery.
Aside from writing off the battery, over-discharging any lithium cell is a huge fire risk. If a cell is overdischarged, they have a tendancy to 'swell', which can break the internal connections and potentially create a short. This short will heat up to a point that the cell is compromised, and then the lithium will react with the water in the atmosphere and make a big fire.
Over charging a lithium battery cell is a huge fire risk. This also causes swelling and over current can also overheat the pack, again compromising the internal structure and creating shorts. Again, remember that this goes for any
single cell, so if your battery isn't balanced you run the risk of having one cell overcharged with the rest reading a lower voltage, making the
nominal voltage less then the fully charged state - therefore your charger will keep pumping current into an already overcharged cell.
I have been running a bare cell 60ah battery from evpower in WA for the last 4 ish years charging off the alternator (no chargers or anything)
No issues other than me flattening it twice and needing to recharge the batttery very carefully to get i back up to a safe charge level
Please say your battery has a BMS built in?