Chem-Packs can be used to increase the Rank of a Lt of the corresponding faction, which boosts their maximum level (Shadow Chem-Packs can be used to boost unaffiliated Lts). The boost they get depends on the level of the Chem-Packs used and the rarity of the Lt, as shown in the table below:
|# of packs needed||Level boost||# of packs needed||Level boost||# of packs needed||Level boost||# of packs needed||Level boost|
Any Lt ranks are retained if you later combine the Lt to increase their stars. Level boosts must be applied in-order (i.e. you can't use level II chem-packs until you've used level I on that Lt, making them rank I). Ranks are always fixed to a particular Lt, even through Fusion, so if you have a Lt at a given rank and you fuse them away, the next time you acquire that Lt, it will have the earlier rank.
There's a summary table showing which bosses drop which chem-packs at Chem-Packs Table.