These two teams met earlier this month in the Scottish Premiership and Livi will be seeking revenge for a 2-1 home defeat as well as some silverware.
They have climbed to fifth place in the league table thanks to a remarkable 14-match unbeaten run that only ended when they lost to St Johnstone on February 6.
A week later they were beaten 3-0 at Dundee United in the league, but recovered somewhat to take a point from a 1-1 draw at St Mirren last weekend.
Martindale's personal story is also something of a fairytale, with the Lions boss having endured some dark times in his life.
He served four years in prison back in 2006 for organised crime-related offences and was also never a professional football player.
If Livi can win the cup on Sunday then his road to redemption will have been completed in a remarkable and inspiring way.
The Lions last won the League Cup in 2004, but just four years later they were down in the fourth tier of Scottish football.
Their rise since then mirrors that of Martindale in many ways, and many neutrals will be wishing them well this weekend.
St Johnstone will not care about any of the romance of Martindale and Livi's story, of course. The Perth Saints are the only team to have beaten Livi since Martindale took over in West Lothian and they will surely take some confidence from that.
Manager Callum Davidson has also asserted this week that his players should take confidence from the manner of their semi-final win over Hibernian.
The Saints beat Hibs 3-0 to reach the League Cup final, in a game in which Davidson felt his team did not start well but then improved hugely as the game went on.
Davidson believes that that performance should tell the players that they belong in a final and should feel confident at Hampden.
They have certainly enjoyed some solid enough form in recent weeks to suggest that they can win on Sunday.
Since reaching the final, Davidson's team have lost just two of their six games, and they were against Rangers and Celtic.
While much of the sentimental focus on this game has been on Martindale, the Perth outfit have all the assets needed to create a legend of their own this weekend.
Livingston Scottish League Cup form: WWWWWW
Livingston form (all competitions): WDWLLD
St Johnstone Scottish League Cup form:WDWWWW
St Johnstone form (all competitions): DWLWLW
Livingston boss Martindale may not be able to call on forward Scott Robinson, who is a doubt with a back injury after limping out of the game against Dundee United a fortnight ago.
For St Johnstone, midfielder Murray Davidson has only a 50-50 chance of playing on Sunday, according to his manager.
The 32-year-old has suffered a setback in his recovery from a calf problem and is very unlikely to start at Hampden, though he could well feature in the squad.
David Wotherspoon will be fit to play, though, after recovering from a groin injury. St Johnstone have no other injury concerns ahead of Sunday's final.
Livingston possible starting lineup:
Stryjek; Devlin, Fitzwater, Guthrie, Serrano; Pittman, Bartley, Holt; Mullin, Sibbald, Reilly
St Johnstone possible starting lineup:
Clark; Kerr, Gordon, McCart; Rooney, McCann, Craig, Booth; Melamed; Wotherspoon; Kane
We say: Livingston 1-2 St Johnstone
Livi's fairytale will end on Sunday when they suffer a narrow defeat to Callum Davidson's Perth Saints.
Extra time will probably be needed and a tight game's outcome could be determined by an error.