One word equivalent to "play with someone's hair"
I don't think you can use one word to say "play with someone's hair", but I think the verb "to caress" does a better job of expressing the idea of him lovingly stroking her hair:
Her head was in his lap, and he was caressing her hair.
Definition:
caress: to touch someone gently in a way that shows you love them
(Longman)
Consider, fondle.
: to handle, stroke or touch lovingly AHD