Primary means non-rechargeable lithium. Use them just like alkaline, but they have a much longer shelf life and are not likely to leak. I use them in things like smoke alarms, thermostats, and some remotes.
CR123A is higher voltage lithium primary, same diameter as a 18650, but about half the length. This kind of light would work well if you wanted a tiny light with better output than AAA. I see not problem keeping them in a car. They are often used in photography where you could ruin very expensive equipment if it leaked.
LiFePo4/lithium-ion phosphate is a type of rechargeable lithium, a bit lower voltage (3.3v) and lower capacity, but is more robust than Li-on. Some people don’t think it’s a good idea to leave Li-on in a car….just in case.
I have a few LiFe from an old use but not sure I’d go out of my way to get them. LSD NiMh is probably more generally useful.
I have a small AAA twisty with a NiMh eneloop that’s easy to get at in the car for regular use in the dark. I also have a AA NiMh eneloop headlamp in the trunk if I have to have hands free and do some work that will take longer or need a lot more light. NiMh are very unlikely to leak. They will slowly discharge so it’s reasonable to pull them out and cycle them 1-2x/year. Decent batteries should still last a long time. Only use LSD NiMh for this, otherwise they will be discharged when you want to use them.