A Draw for White in Smeets - Vachier-Lagrave?

Jan Smeets has had a tough time of it in the Tata Steel tournament this month.  (I am sure that I am not the first to mention it, but doesn't "Tata Steel" sound like a porn star name?)

In the eighth round, Smeets had White against Maxime Vachier-Lagrave (who sounds like a Bond villain).  Lagrave played a Modern Defense with 4...a6, which I used to consider daring and exciting long ago when I played it with Black, but also slightly insulting when I faced it with White.  In any event, Smeets looked, if anything, better out of the opening, and was certainly no worse until he played 21.Rd8?  But, in his usual ferocious time trouble, he wound up defending a difficult pawn-down rook ending, which he proceeded to lose.

I want to suggest that at move 38 (when he probably had seconds left on the clock), Smeets missed a good drawing chance.  At this point, after some exchanges, the material was even, though Black had a strong passed pawn on the kingside.  In the following position,

Smeets played 38.Kb3? and wound up in a very difficult position after 38...Kc6 39.h4 Kd5 40.h5 Ke4 41.hxg6 Rxg6.  He may still have had a draw even then, but I think the draw is more likely after:

38.h4!