Palmer is to play in Sunday’s friendly against Motherwell as the Easter Road side weigh up their options for their number one jersey.
Oxley featured in last night’s 6-1 win over Edinburgh City at Meadowbank Stadium, but the Englishman is expected to return south to join up with his former Hull City manager, Phil Brown, at Roots Hall.
Arriving in the capital in his place could be Palmer, a 19-year-old goalie who has been on the bench for West Brom on a couple of occasions and was farmed out to Kidderminster Harriers in the National League last year.
Lennon said: “We’ve got a goalkeeper in Alex Palmer from West Brom, we’re going to have a look at him at the weekend.
“We’ve had permission from West Brom and the SFA to play him and we’ll give him a run out on Sunday.
“I would imagine Mark will be going to Southend.”
Goals from Darren McGregor, Jason Cummings, Sam Stanton, Dylan McGeouch, James Keatings and Danny Handling handed Lennon his first win in charge of Hibs against SPFL newcomers City.
Lennon added: “I thought we were excellent. There was good attacking intent and good intensity to our play and we got six goals, and could have got a lot more. The attitude of the players was excellent.”