Lithium Ion and Lead Acid battery in series
What you propose should work technically and is probably not too hard to do "well enough" as long as you are sensible [tm]. 

As Peter says, mixing battery chemistries can often have bad outcomes, but as long as you do not violate basic requirements this could be reasonably problem free. 

It is not obvious why you would use a LiIon second battery - lead acid will better match the cost/capacity and general cycle lifetime for given use.
If your main battery was say about 50 Ah (less than 1 hour at 50 A due to C rating usually being at 10 hour rate or even lower) and you wanted both batteries to work together throughout the LiIon battery would also need to be 50 Ah or more. That's not a small battery and you are going to need a separate specialist charger to charge it - which is OK if you have the equipment already - but otherwise adds expense and complexity. You may be able to obtain 2V indivual LA cells or a 4V battery (they do exist) but again are faced with the charging issues mentioned below. 

A LiIon battery MUST have it's low voltage discharge limited to a safe voltage. It MUST be rated to discharge safely and continuously at say 50A.
Max charging current is liable to be 25A or 50A (or other - varies with manufacturer). You COULD safely enough [tm] charge a single LiIon cell by limiting Imax to at or below rated max value and setting maximum charge voltage to say 4V or slightly less. You can then allow it to charge until 4V is reached and can float it at 4V "safely". This charges to noticeably below max capacity and increases cycle life. You MUST NOT charge it all the way to 4.2V and float it there - battery death happens soonish.

Note that LiIon will have 4.2V (if fully charged) to start and 3V or so fully discharged. (Lower possible but unwise if long cell life is wanted).