This will be the second meeting between the teams this season, with Scott Pittman and Owen Moffat scoring second-half goals for either side to force a share of the spoils in their league clash on August 24.
Match preview
Livingston's solid second-half display at the New Douglas Park saw them return to winning ways in the Scottish Championship as they picked up a 3-1 victory over Hamilton Academical on Saturday.
Kevin O'Hara hit back for Hamilton Academical within 60 seconds of Stevie May's 40th-minute opener to end the first half level but Lewis Smith and Andy Winter found the target after the break to hand the visitors all three points.
Before that, Livingston suffered their first league defeat of the season on October 29, when they were beaten 3-0 by Dunfermline Athletic at the East End Park, four days before playing out a 1-1 draw with 10-man Queen's Park.
David Martindale's men have picked up seven wins and five draws from their 13 matches to start the Championship campaign, claiming 26 points from the first 39 available to sit second in the table, six points off league leaders Falkirk.
The Lions now turn their focus to the Challenge Cup, where they were spared their blushes in the fourth round as they needed penalties to see off League One outfit Inverness Caledonian Thistle at the Almondvale Stadium on October 12.
Having kicked off their cup quest with a comfortable 2-0 victory over fourth-tier The Spartans in the third round on September 7, Livingston were held to a 2-2 draw by Caley Thistle in normal time before winning 5-4 on penalties, with Robbie Thompson missing the decisive kick for visitors.
Greenock Morton, on the other hand, failed to find their feet in the Championship as they were held to a 1-1 draw by Ayr United when the sides squared off at the Cappielow Park last Saturday.
Iain Wilson broke the deadlock in the 37th minute to hand the home side a first-half lead but English striker George Oakley restored parity with a well-drilled effort five minutes after the break to force a share of the spoils.
With the weekend stalemate, Greenock Morton have failed to taste victory in their last five league matches, claiming two draws and losing three, including a 6-0 hammering against Falkirk at the Falkirk Stadium on November 2.
While results have been hard to come by in the Championship, where they currently sit eighth in the table, Dougie Imrie's side have enjoyed a solid Challenge Cup run so far, brushing aside Cowdenbeath and Hamilton Academical to reach the quarter-finals.
Morton kicked off their cup campaign in the third round with a 1-0 victory over Cowdenbeath at Central Park on August 7 before beating Hamilton by the same score line in the fourth round courtesy of a first-half penalty from former Watford man Filip Stuparevic.
While the Ton will be looking to go at least one better than their quarter-final exit from the Challenge Cup last season, they have been drawn against an opposing side whom they have failed to get the better of in any of their last seven competitive meetings, losing four and claiming three draws since a 2-1 win in April 2016.
Livingston Scottish Challenge Cup form:
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Livingston form (all competitions):
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Greenock Morton Scottish Challenge Cup form:
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Greenock Morton form (all competitions):
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Team News
Pittman was forced off injured midway through the first half against Hamilton on Saturday and the experienced midfielder is a major doubt for the midweek cup clash.
While Piitman, who picked up the Lions' October Player of the Month, will be a big miss on Tuesday, Reece McAlear should come into the form, teaming up with Stephen Kelly and Andrew Shinnie at the center of the park.
May, Smith and former Ipswich Town man Tete Yengi should lead the attack while Mathew Clarke, Ryan McGowan, Michael Nottingham and Jamie Brandon should retain their roles at the opposite end of the pitch, with Jerome Prior starting in goal once again.
Greenock Morton came out unscathed against Ayr at the weekend and Imrie could name a similar starting side at the Almondvale Stadium, with Cameron Blues, Jack Baird, Kirk Broadfoot and Morgan Boyes forming the back four.
Stuparevic has started six of the season matches since completing a loan move from Motherwell in September and the Serbian striker should spearhead Morton's attack once again, alongside Moffat and Michael Garrity.
Livingston possible starting lineup:
Prior: Clarke, McGowan, Nottingham, Brandon; Kelly, Shinnie, McAlear; May, Smith, Yengi
Greenock Morton possible starting lineup:
Budinauckas; Blues, Baird, Broadfoot, Boyes; Wilson, Gillespie. Lyall, Moffat, Garrity; Stuparevic
We say: Livingston 3-0 Greenock Morton
Buoyed by their impressive result against Hamilton, Livingston will return to cup action with high spirits before their Championship top-of-the-table clash against Falkirk on November 16.
Having lost their last two away games, conceding nine goals and failing to hit the target across both outings, Morton are in for another tough 90 minutes on Tuesday and we see them struggling at the Almondvale Stadium once again.