Lithtech was part of Monolith as far back as the days when Blood 1 was in development. Originally, the Lithtech egnine was somehow connected with Microsoft (I forget how, I think they were developing it for M$), but then during the development of Shogo, Monolith gained exclusive rights to Lithtech from Microsoft.
The guy who wrote Lithtech was stolen by Valve, & it has been speculated that TF2 will be powered by whatever that guy codes up for them.
Then later, Jason released some statement that since he was getting too busy, Lithtech was becoming a separate entity from Monolith, and that he had full confidence in the new CEO of Lithtech.