Lovett, 28, has put pen-to-paper on an initial one-year contract, with a further one-year option.
He was Welling United’s outstanding performer and multiple player of the year award winner in National League South in 2024-2025.
Lovett will replace Gregory, who has not been able to commit to a full-time future with the Pilgrims.
Shropshire-based Gregory is expected to join a club nearer home - and departs with the Pilgrims’ best wishes following a brilliant two-and-a-half year spell in Lincolnshire.
Gregory recorded 33 clean sheets in 91 appearances for the Pilgrims, earning promotion to the National League in 2024, either side of ultimately successful relegation battles in Steps 2 and 1.