Two goals from Southwell and a third from Charley Sanders at close-range sealed a comfortable win on Wednesday evening.
United fielded a strong side with four trialists included in the squad and were dominant although Lincoln did score a consolation goal in the final moments of the game through Gio Carchedi.
Boston opened the scoring on 39 minutes when SOUTHWELL, through on goal, drove the ball low under Robert Peet into the bottom corner from a long throughball.
Earlier in the half both Southwell and Carl Piergianni had opportunities from headers in the box which hit the bar and went just over respectively.
The second half saw the Pilgrims more dominant in the Lincoln final third and on 63 minutes SOUTHWELL scored his second from an excellent 25-yard finish.
Boston then grabbed a third on 80 minutes when SANDERS tapped home from close-range following Southwell's initial effort on goal.
Second half substitute CARCHEDI scored a consolation goal for Lincoln on 90 minutes.
Boston (4-4-2): Sam Vince; Zak Mills, Duran Reynolds (Connor Smythe 72), Scott Garner, Carl Piergianni; Kaine Felix (Kieran Wallace 60), Conor Marshall (Michael Hollingsworth 68), Danny Meadows (Stefan Galinski 60), Jamie McGhee (Charley Sanders 72); Dayle Southwell, David Fallah (Jack Barlow 60). Sub (not used): Andy Hewitt.
Lincoln United (4-4-2): Robert Peet; Sean Wright, Ben Brown, Liam Richardson (Brendan McDaid 69), Callum Ward; Michael Jacklin, Lewis Chambers, Daniel Brooks, Bruno Holden; Nathan Modest (Gio Carchedi 46), Sam Duncum (George Asplin 20). Sub (not used): Nathan Burrows.