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'Michail is conscious and communicating and is currently under close supervision at a central London hospital,' the club posted.
He will take charge on July 1 after Moyes left the east London club by mutual consent.
Liverpool remain third on 75 points, one behind second-placed Manchester City, who have played two games fewer, and two behind first-placed Arsenal, who have a game in hand and a much-superior goal difference.
It was a sublime display by Arsenal who wiped off a goal difference deficit to champions Manchester City who they joined on 52 points, although they stay in third place courtesy of scoring fewer goals.
Second-placed Arsenal remain on 40 points, two behind Liverpool who beat Burnley 2-0 on Tuesday.
The goal made Bowen the first English player to score the winner in a major European final since Arsenal's Alan Smith in 1994 and capped a campaign in which West Ham were unbeaten in 15 UEFA Europa Conference League matches.
Arsenal have 74 points from 31 games with reigning champions Manchester City on 70 having played a game less.
Lampard's last game in charge was Saturday's 2-0 league defeat at West Ham United, which kept Everton second-bottom of the table on 15 points after 20 games, above Southampton on goal difference, and two points adrift of the safety zone.
Jarrod Bowen had scored twice in the first half to give West Ham a 2-0 lead.
John Lundstram struck 10 minutes from time to give Rangers a 3-1 win over RB Leipzig and send them into the final 3-2 on aggregate after a see-saw clash at a rocking Ibrox.
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