Suppose $G$ is a finite group, and $l$ is a prime, with $l$ coprime to the order $|G|$. (Thus we have complete reducibility for $G$ representations.) Is there a straightforward condition on $l$ which ensures that every irreducible representation of $G$ is liftable to a characteristic zero representation? (For instance, does the fact that we assume $l$ coprime to $|G|$ suffice?)
Another sufficient condition is that if $G$ is solvable, then for every prime $l$, every absolutely irreducible characteristic $l$ representation can be lifted to the complex numbers. In fact, solvability is not really necessary; $l$-solvability suffices. This is the Fong-Swan theorem.
Added later: Since groups with order not divisible by $l$ are trivially $l$-solvable, this sufficient condition includes, and is more general than the the condition stated by Pete L. Clark.