The new Everton boss sends his side to Nicosia on Thursday in their final Europa League game of the season with first-team coaches Craig Shakespeare and Duncan Ferguson taking charge as he has not made the trip due to a pre-arranged medical appointment.
Everton have had a very poor season and it seems like they are now in a relegation battle in the English Premier League.
Ireland midfielder James McCarthy is likely to return to the Everton starting line-up as Allardyce tests the strength of his squad before the January transfer window.
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Their concluding clash in Cyprus is a dead rubber for both teams as the hosts, with just three points to their credit, can not qualify for the last 32 either.
"The team for Sunday hasn't been picked so there is an opportunity as always in any training session for things to change", Shakespeare told reporters in a press conference held on Wednesday afternoon.
Harry Charsley and Fraser Hornby start for their debuts while Alex Denny, Nathan Broadhead, Stephen Duke-McKenna, Michael Collins and Anthony Gordon join Lavery on the bench, hoping to get the nod for their first appearances.