Hamilton had their chances to go in front before Lyle killed off his former club when he scored midway through the second half following a corner.
Dumbarton joined Queens in tomorrow's fourth round draw with a 2-1 win over Cowdenbeath at Bet Butler Stadium.
Jordan Kirkpatrick scored twice and also hit the crossbar with Cowdenbeath's goal coming from Greg Stewart.
Kevin Watt came off the bench to put Clyde into the fourth round as they saw off Brora Rangers 2-1. Zander Sutherland struck early for the Highland League side before Stefan McCluskey equalised with a cool finish. Clyde finished strongly with Watt netting.
Dunfermline Athletic eased through 5-3 at Elgin City, two late goals from the home side giving a gloss on their performance.
Jamie Duff scored to give Elgin an early lead with a looping a header over Ryan Scully.
But Ryan Wallace scored twice and substitute Jordan Moore also netted a double, his first from a penalty, to make it 4-1.
Alex Whittle scored a fifth before Dennis Wyness and Dachi Khutsishvili scored.
Alloa Athletic had to wait until the second half before they found the net against Inverurie Loco Works, but then eased to a 3-0 win, Kevin Cawley, Ben Gordon and Alex Salmon all on target.
Fraserburgh enjoyed a shock 2-1 win over Montrose with Grant Noble scoring in the final minute. Montrose scored first through Ross McCord, but Graham Johnston equalised and then Noble settled it.
Ten-man Stranraer also had to rely on a last-minute goal - from Jamie Longworth, his second of the match, to give them a 2-2 draw with Auchinleck Talbot.
Auchinleck raced to a two-goal lead through Brian Young and Keir Millican, but Longworth pulled a goal back ten minutes from half-time with a header before scoring to save the tie.
Stirling Albion brushed aside Turriff United 3-0 with Ross Forsyth, an own goal from Stuart Cumming and Mark Ferry contributing the goals.
Ayr United came from behind to beat Queen's Park 3-2.
Queen's went in front when Jamie Brough headed in after 27 minutes, but Anthony Meranghi thumped home the equaliser before half-time. Alan Lithgow put Ayr in front early in the second half and Craig Malcolm scored the third before Spittal pulled a goal back for Queen's Park.
Forfar beat East Fife 2-1 after Dale Hilson scored on the stroke of half-time to give them the lead and Chris Templeman made it 2-0 midway through the second half before Craig Johnstone pulled a goal back.
Keiran Brannan saved Annan Athletic with an injury-time goal at Stenhousemuir.
Martin McNiff gave Annan the lead, but Errol Douglas equalised for Stenhousemuir. John Gemmell then scored from just outside the area to put Stenhousemuir in front, but Brannan had the final say.
Culter and Berwick Rangers must also do it all again after a hard-fought 1-1 draw.
Steve Notman put Berwick in front but an own goal by Mick Dunlop ensures Culter another shot in next Saturday's replay.
Brechin City defeated Arbroath 2-0 at Gayfield with goals from Andy Jackson and Alan Trouten.
Albion Rovers beat Deveronvale 1-0 with Mark McGuigan scoring the only goal after 73 minutes following good work by Liam Cusack.