Smith has started the county season in excellent form with the bat, scoring 401 runs including two centuries.
He has kept wicket for all 20 of his Tests for England since making his debut in 2024, but he has played second fiddle at county level to Foakes, widely regarded as the superior wicketkeeper.
However, the 33-year-old came out of the Essex game with an injury having bowled two overs at the end of the match on Monday as things were petering out towards a draw.
Lawes has been considered as a possible to make the England squad for the first Test with New Zealand on 4 June, but he has only managed seven wickets in three games that have all finished as high-scoring draws.
Another player to miss out at The Oval over the next few days will be Gus Atkinson, with the England bowler rested as part of his ECB central contract.
