Kyle has scored 10 goals in 56 appearances at Turf Moor and five goals in 16 internationals.
Laws also fined midfielder Kevin McDonald for leaving Turf Moor without permission at half-time during that game.
Burnley have been without a manager since Steve Cotterill left Turf Moor by mutual consent on 8 November.
Last week Burnley boss Owen Coyle said Lafferty had made it clear he wanted to leave Turf Moor.
Burnley's boss arrived at Turf Moor a free agent after he parted company with Sheffield Wednesday in December.
Laws has lost 14 of his 17 games since taking over from Owen Coyle at Turf Moor in January.
With Burnley signing Danny Fox from Celtic, Easton has been pushed further back in the Turf Moor pecking order.
Eagles was having an outstanding night, and he brought Turf Moor to its feet with another long-range shot that flew just over.
Glen Little grabbed his first goal of the season to give Burnley a deserved victory over Wimbledon at Turf Moor.
Rangers had offered Alan Gow as part of the deal and the midfielder remains in talks with the Turf Moor club.
The club fined midfielder Kevin McDonald after he left Turf Moor without permission at half-time in last Saturday's Manchester City mauling.
Liverpool, who are still chasing a Champions League spot, face Burnley at Turf Moor while Fulham take on Everton at Goodison Park.
Dimitri Papadopoulos' shocking miss from close range cost Burnley the chance of victory against the First Division's form team at Turf Moor.
The Turf Moor outfit hit back and went close through new signing Charlie Austin and missed headers from Rodriguez and Clarke Carlisle.
Mark McGregor scored his first league goal for Burnley to put them on their way to victory against promotion-chasing Norwich at Turf Moor.
Saturday's contest was the first match at Turf Moor since the Clarets appointed Eddie Howe as manager on 16 January, on a three-and-a-half-year contract.
Burnley looked like they might be in for a long night at Turf Moor after Cesc Fabregas capped a scintillating Arsenal opening salvo with an early goal.
Burnley fans are being asked to arrive at Turf Moor by 09:45 GMT, so they can be taken to Ewood Park ahead of the match.
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And, while leaking goals and being outplayed on their travels, they have taken the prized scalps of Manchester United and Everton with their Turf Moor form.
The buses set off from Turf Moor at 1900 BST and headed along Yorkshire Street, Centenary Way and Finsley Gate before arriving at the town hall.
Coyle decided to remain at Turf Moor after leading the Clarets into the English Premier League, while Martinez opted for the lure of his former club Wigan.
Burnley boss Coyle, thought to be Celtic's top target, is now close to agreeing an extension to his contract at Turf Moor, according to the Lancashire club.
Former Sheffield Wednesday boss Laws has endured a tough time at Turf Moor since taking up the reigns in January following Owen Coyle's departure to manage Bolton.
In the other Premier League game on Sunday, promoted Burnley followed their 1-0 win over Manchester United by beating struggling Everton by the same scoreline at Turf Moor.
And while counterpart Harry Redknapp will not regard the second leg at Turf Moor as a formality, it will take a miraculous effort from Burnley to reach Wembley.
Like Dowie, Laws believes the shock of last weekend's defeat at Turf Moor, in which they conceded four goals in the first 20 minutes, might galvanise his side.
Midfielder Kevin McDonald was fined after he left Turf Moor without permission after he was substituted at half-time of the 6-1 mauling by Manchester City on 3 April.
Villa had not won in 22 league and cup matches at Turf Moor dating back to 1936 and their prospects of ending that sequence suffered when Caldwell struck.
But Turf Moor has proved something of a graveyard for visiting teams this season, so it was no surprise that Burnley refused to go quietly, even when confronted by Arsenal's early superiority.
Burton had defeated another Championship side in Middlesbrough to reach the fourth round of the competition for the first time - and the Brewers gave it a real go at Turf Moor.
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