My thoughts, as a LenDale White dynasty owner... I'll try not to be too biased...
Henry has has 2 terrific games in a row. And its probably safe to expect another nice week against Houston. The Texans D is really getting hit by injuries. And even healthy, they were pretty weak against the run.
If White is healthy, Expect Henry to take 20 carries, White 8-10. If there is a rushing TD, I expect Henry to get it.
Beyond this week, things get a bit cloudy. Jacksonville, Baltimore, Philly and the Giants. Jax D has some injuries too, and Henry will probably be good for 80, maybe a TD. But those 3 next games promise to be brutal. The Ravens D should be able to shut the Titans running game down. Philly and NYG could easily jump ahead with big leads and force the Titans to pass.
If Henry doesn't produce in those last 3, expect White to push the split to 50-50, if not take the job all together. If Henry DOES survive those 3 games with decent production, he might stick around for a long, long time.
But, at some point, White will be getting double digit carries. Chris Brown will leave as a free agent. To retain Henry, the Titans will have to pay a large (something like $5 million, I think) bonus in the spring. Before they spend that kind of cash on Henry, they will want to see what White can do.
I'm rooting for White. Logic says White will get a shot. But really, its a toss-up. If Henry keeps producing, it'll be tough for the coaches to pull him.