Substitute 12v Lead Acid Battery with Nominal 10.8v Lithium Ion Battery?
Not a good idea, unless you are planning to replace the charging circuitry as well. 

Regardless of the circuitry being able to operate at a lower voltage, which is not guaranteed, lead acid batteries are very forgiving in how they are charged and handled tolerating relatively large voltage variations. Lithium batteries not so much, and a fire is a very real possibility. 

A battery has a fixed voltage range given its chemistry, these are not electrically “tunable” in any way.