The Pilgrims will be seeking to get their first away points on the board when they travel to the Phillips 66 Community Stadium after defeating Guiseley 1-0 at The Jakemans Stadium on the opening day.
Andre Johnson's 76th minute strike accounted for the Lions while Leamington were picking up a creditable 2-2 draw at Altrincham first up.
United are expected to select from an unchanged squad for the trip to Warwickshire, with Jay Rollins being Craig Elliott's only definite absentee.
Leamington have a largely unchanged squad from last season, but have recruited attackers Matt Stenson and Connor Taylor during the summer months.
Last season's corresponding fixture ended 2-0 to the Pilgrims courtesy of goals from Brad McGowan and Ashley Hemmings.
Tuesday's match referee is Barry Lamb, who took charge of the Pilgrims' final away fixture of last season against Nuneaton Town.
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