Potts, who made his Test debut in the first match of the 2022 summer, also against New Zealand at Lord's, impressed with his 20 wickets at 28.00 in the first five matches under Ben Stokes' captaincy.
However, he did not feature in the final two matches of the summer against South Africa following the return to action of Ollie Robinson, and was a surprise omission from England's squad for the Pakistan tour.
Lawrence, meanwhile, is back in the set-up for the first time since the tour of the Caribbean last March, on which his spirited batting displays - including scores of 91 and 41 in Barbados - proved to be an early indication of the team's future direction of travel. However, he suffered a dip in form for Essex in 2022, exacerbated by a pair of hamstring injuries.
He has a chance to be England's pace spearhead on the trip, following the decision to rest Mark Wood in the wake of his key roles in the second and third Tests against Pakistan this month.
Wood, who was also a major in England's successful T20 World Cup campaign, is due to take a break from all international and franchise cricket in January to fully recover after a busy winter in all formats. He is expected to tour Bangladesh in March, where England play three ODIs and three T20Is, and is likely to be available for the IPL too.
Rehan Ahmed, England's 18-year-old matchwinner in Karachi last week, has not been included in the squad, as part of his management for the winter. He is instead set to play for Gulf Giants in the ILT20 in the UAE in January, and could be in the frame for the Bangladesh white-ball tour too.
With another year of competing demands looming for England's multi-format players, Joe Root has been included in the tour, but will be limited to a handful of games for Dubai Capitals in the ILT20 between now and then, with England seeking to managed his workload ahead of the defence of the 50-over World Cup in India in November 2023.
England Test squad: Ben Stokes (capt), James Anderson, Stuart Broad, Harry Brook, Zak Crawley, Ben Duckett, Ben Foakes, Will Jacks, Dan Lawrence, Jack Leach, Ollie Pope, Matthew Potts, Ollie Robinson, Joe Root, Olly Stone