He applied his contact lenses.
He put in his contact lenses.
He put his contact lenses in. (but not "in[to] his eyes")
This is one case where, even though the lenses go onto or on the cornea, we use 'in' (generally).
You put glasses on. You put hearing aids 'in' or 'on'. (You don't need to mention eyes or ears, since there's only one place these devices are supposed to go).