Rovers will take on the Lions on Saturday, April 3 at the Tony Macaroni Arena with a 3 o’clock kick off.
Raith boss John McGlynn says he’s looking forward to facing his old club, where he was manager between 2013-14, and is hoping for some revenge after Rovers were knocked out of the same tournament by David Martindale’s side by 3-1 last year.
Rovers were leading 1-0 at half time before Livi struck back in the second half.
"We played them last year so it's an opportunity to go through there and have another go at them,” he said.
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The cup draw has also led to a fixture change for the Stark’s Park side.
Queen of the South’s match with Hibs has been chosen to be televised live on BBC Scotland on Monday, April 5, meaning that Rovers scheduled trip to Dumfries the following night has been pushed back a week to Tuesday, April 13, 7pm kick off.
Also being shown live on television are; Ross County v Inverness Caledonian Thistle (Friday, April 2, 5.35pm, BBC Scotland), Dumbarton v Aberdeen (Saturday, April 3, 12.15pm, BBC One Scotland), Celtic v Falkirk (Saturday, April 3, 7.30pm, Premier Sports) and Rangers v Cove Rangers (Sunday, April 4, 6.30pm, Premier Sports).
The reamaining fixtures, all to be played on Saturday, April 3, are; Ayr United v Clyde, Brora Rangers v Stranraer, Dundee United v Partick Thistle, Dundee v St Johnstone, East Fife v Greenock Morton, Forfar Athletic v Edinburgh City, Formartine United v Motherwell, Fraserburgh v Montrose, Hamilton Academical v St Mirren and Stenhousemuir v Kilmarnock.