Mr Lewis was speaking hours after the conclusion of a Stormont election which saw an historic victory for Sinn Fein to become the largest party and win the entitlement to nominate a first minister.
Sir Jeffrey has called for action on the Northern Ireland Protocol before re-entering the executive.
Mr Lewis is to meet with the leaders of the Stormont parties on Monday to talk about resurrecting the Assembly.
Appearing on the BBC’s Sunday Politics programme, he said it is widely acknowledged there are issues with the protocol that need to be resolved.
He also pointed out that the full protocol has not yet been implemented with a number of grace periods running on aspects of the post-Brexit treaty.
Unionists strongly oppose the protocol as placing a border in the Irish Sea.
Mr Lewis restated his position that the Government would like to reach agreement with the EU over resolving issues with the protocol, but said nothing has been taken off the table.
He urged Sir Jeffrey to nominate a deputy first minister to get devolved government fully working again.
The executive has been unable to fully function since February when the former first minister Paul Givan resigned as part of the DUP’s call for action against the protocol.
“It’s for the UK Government to do the negotiations, Jeffrey and the DUP and all parties in Stormont should together and bringing Stormont back to deliver on the domestic issues for Northern Ireland,” he said.
Meanwhile, Mr Lewis appeared to rule out calling a border poll, saying that while the first nationalist First Minister is a significant moment, the nationalist vote overall has not grown and the unionist vote remains larger.
Appearing on the same programme, DUP MLA Jonathan Buckley responded saying his party stood on a promise to remove the protocol.
“Let me be very clear … either the Secretary of State wants an Executive or the protocol, but he can’t have both,” he said.
“The Secretary of State has a very clear choice.”
Meanwhile Sinn Fein MP John Finucane said he was shocked anyone could deliver a message that the return of the Executive can wait amid a cost-of-living crisis and needed health service reform.
“There’s over £300 million sitting there, ready to go into people’s pockets, and I think it’s incumbent that we sit down collectively, because that’s what people want,” he said.
Sinn Fein has won 27 seats while the DUP has 25, the Alliance Party 17, the Ulster Unionists (UUP) nine and the SDLP eight, with four others elected.
Mr Finucane described an “excellent return” for his party, but added they could have picked up another couple of seats in some constituencies which ended in close final counts.
Mr Buckley said it had been “quite a good result” for the DUP, particularly given some predictions that his party could drop to 18 seats.
He called for unionism to have a conversation with itself, adding “divided unionism in 2022 cannot win elections”.
Alliance MLA Sorcha Eastwood said it had been a “fantastic election” for her party, doubling their MLA count.
“It’s not just a brilliant day for Alliance, it’s a good day for Northern Ireland as well because people came out and voted positively and that’s a really important thing that shouldn’t be lost in the noise,” she said.
UUP MLA Robbie Butler backed his leader Doug Beattie, who had a close run in Upper Bann to retain his own Assembly seat.
Mr Butler said Mr Beattie had been leader for less than a year before the election, he insisted his message is strong, and described him as an “excellent leader”, vowing to continue to offer positive unionism.
SDLP MLA Matthew O’Toole said his party had been on the wrong side of the tide in this election.
He described a move within nationalism for Sinn Fein after the DUP “behaved appallingly” in the pre-election period by refusing to confirm whether they would nominate a deputy First Minister to serve with a first nationalist First Minister.
Mr O’Toole said the SDLP had run a positive campaign with great candidates, but added: “Unfortunately it didn’t work for us this time.”