Some specific info ...

Yes, the VANOS (that adjusts the camshaft timing) is controlled with engine oil, at pressure, controlled by the VANOS solenoids to actuate the VANOS helical gear cups to actually move the cam sprockets with respect to the camshafts.

So if the engine oil ran dry enough, all bets would be off regarding VANOS. I don't think any permanent damage could result (either the VANOS burning up, or the possibility of driving the camshafts to create piston-valve impact). The camshafts could have been left in an adjustment state that could cause misfires.

But some sort of resetting may very well be required. If you don't have special OBD tools to do this, you might just try disconnecting the battery for a while.

If you're lucky, the "running like crap" was due to VANOS mis-timing rather than any significant internal engine damage.

In general I would not give up hope. Good luck to you and your Mom.

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2001 X5 3.0i, 203k miles, AT, owned since 2014