Mixing Lead acid and Lithium ion in series, after charging them separately
Without further details it is difficult to tell.

Anyway, there is a BIG caveat: jump starting a veichle requires very high current spikes, and the cells in the string must be able to withstand it.

If the lead acid batteries you will use are of the starter type (and not of the deep cycle type, as used e.g. in UPSs) they are designed to provide current pulses that are even hundreds times greater than their normal current rating (e.g. a 50A rated battery could provide 1000A pulses for a couple of seconds).

This is a problem with LiIon cells, which usually can't survive such pulses. You might think that putting in series an equally rated 50A LiIon battery would do, but probably that battery could survive just a 200A pulse, and maybe for only a few milliseconds).

Moreover, the internal impedance of the LiIon cells could be greater than that of the Lead Acid battery, so you end up with a pulse of power being dissipated in the LiIon that could raise its temperature above safe limits.

See this comparison table between rechargeable batteries at BatteryUniversity.

TL;DR: you should get the datasheets of both the Lead Acid battery and of the LiIon battery and examine their characteristics. Only then you/we could tell if what you have in mind will be safe to do.

SAFETY WARNING: lead acid batteries are quite rugged and they can withstand even strong overloads for a short time. LiIon CAN'T DO THAT Overloading a LiIon cell could heavily damage it, which in turn could make the battery explode or vent with flames!!! Don't try your experiment without knowing the characteristics of your batteries. You don't merely risk to damage your batteries, you risk your life (especially with big LiIon battery packs)!