The Hammers have seen their push for Champions League football falter recently having slipped to two defeats in their last three top-flight games.
But a return to winning ways against struggling Everton would mark the first league double over the Blues since 1972/73.
Lampard's side are in dire need of points, just three above the relegation zone, but a late 1-0 win over Newcastle before the international break ended a run of five straight Premier League defeats.
West Ham v Everton: Date and time
This Premier League clash will take place on Sunday, April 3.
The match at the London Stadium will kick off at 2pm.
A second-half winner from Angelo Ogbonna was enough to separate the two sides in the reverse fixture back in October.
West Ham v Everton: TV channel and live stream
This match will be broadcast live on Sky Sports Main Event and Sky Sports Premier League with live coverage starting from 1pm.
Sky Sports customers can live stream this via the app using their mobile, tablet or computer devices.
If not, you can purchase a Sky Sports Day Pass from NowTV for £9.99.
West Ham v Everton: Team news
The hosts have been handed a huge boost by Jarrod Bowen stepping up his recovery over the break but this game might come too soon for him.
Ogbonna, who scored against Everton in the reverse game, is a long-term absentee for David Moyes' side.
Lampard, meanwhile, will be without midfielder Allan for the first of his three match ban after he received a red card against Newcastle.
Everton already are in the midst of an injury crisis at the club, with Tom Davies, Yerry Mina, Tyler Onyango and Andros Townsend all sidelined.