You can use LiFePO4's but it would be best if they were self-heating types. Contrary to common belief, these batteries don't automatically "die" below freezing. They can't be charged below freezing, but their BMS controllers will prevent that anyway. But you lose a lot of "usability" because when the BMS shuts the battery down to protect it, the battery goes offline until it's warm again. (And self-heating pads consume current as well.) So I personally would only use a LiFePO4 in a more protected environment, like a camper or RV, or in summer where freezing temps overnight are unlikely anyway.
So on that side yes, I think a deep-cycle lead acid is best, ideally an AGM.
For wattage, every unit is different but most chest freezers will take ~400Wh/day. It's quite a range - 200-800 - but let's say 400Wh for the sake of the argument. But now let's adjust it because we aren't trying to freeze anything, so if we change the setpoint to say 38F (a common fridge temp) maybe we'll only need 320Wh/day.
Deep-cycle batteries should not be discharged below 50% of their rated capacities if you want them to live very long, despite their names. So let's say you have a 500Ah battery (kind of on the small side actually), so we'll use 250Ah as its max "capacity". P=E*I so at E=12V and I=250 that's 3000Wh of capacity. With no solar input at all, and a chest freezer "sipping" current in "fridge mode" you could in theory run that thing for over a week on a single battery. Screw a single solar panel to the lid of the freezer and you've got a pretty self-sustaining setup for most environments. You'll need a small charge controller and inverter, and those will have some losses, but either way you can see this is a pretty sustainable setup for a modest cost.
FWIW if you have a vehicle that you don't mind idling once a day (not a diesel) and a pair of jumper cables or a 7-pin trailer connector with an active 12V AUX wire, you could just use your vehicle to recharge the setup instead of solar.