The result leaves them in third place seven points adrift of their rivals who remain on course to take the championship for the fourth-successive year.
Goals by Luke Howsen, Joel Timmins and Paul Wilkins earned the three points for LMS while Craig Gregory and Lee Thompson were the marksmen for Cononley.
A hat-trick by Ben Gorman powered second-placed Trawden Celtic to a 4-0 win at Cross Hills which keeps them three points behind LMS. Mark Whitfield was also on target.
Former Barnoldswick Town striker Liam Garbutt netted twice as Rolls defeated relegation-threatened Emb-say 3-2.
James Cumstey was also on target for Rolls while Alex Conroy and Fred Midgley replied for Embsay.
Wilsden suffered an 8-0 thumping at Grindleton where Richard Hodges netted a hat-trick.
Player-manager Shaun Airey scored twice while Elliott Firth and Pedro Quintas added further goals.
Zak Holgate scored for Chatburn with Stuart Gee replying for Grassington.
Hellifield Sports eased their relegation fears with a 4-2 win at fourth-placed Pendle Renegades.
Dale Denham’s double was added to by Steven Procter and Carl Stanford for Hellifeld, while Owen Pearson scored both the home side’s goals.
Bingley Town drew level on points with AFC Colne at the top of Division Two after defeating them 3-1 with goals by Michael Judson (2) and Kyle Richmond.
Colne remain top by virtue of a superior goal difference, but Bingley havw a game in hand on their rivals. Skipton Town are the dark horses in the title battle.
They are three points behind the top two but have two games in hand on Bingley and three on Colne after winning 1-0 at Earby Reserves thanks to a solitary strike from Liam Cartman. At the other end of the table, Skipton LMS Reserves eased their relegation fears with a 3-1 victory over Cononley Sports Reserves with goals by Chris Armitage, Michael Conroy and Joseph Parker. Robert Slater replied.
Bradley had a comfortable 4-0 success at Rolls Reserves where James Wilson (2), Robert Watson and David Jaz were on target.
Oxenhope Rec produced one of the results of the day as they defeated Division Three leaders Grassington United Reserves 5-0 in the clash between the top two to record their seventh-successive win.
The only goal of the first half came when a corner from James Bailey was passed into the net by Nivard Trowers. Ten minutes into the second period a long throw from Andy Fox saw Connor Madden head in and soon after Oxenhope made it three when good work by Liam Gill set up Ellis Atha. In-form striker Tony Cooper smashed number four into the bottom corner before Tom Brown rounded the keeper to coolly stroke in the final goal.
Despite their win, Oxenhope are eight points behind the leaders but do have a game in hand.
Two goals from Aatir Zuber and one by Aaran Abbas enabled FC Sporting Keighley to edge out Cowling Reserves 3-2. Luke Barker and Martyn Dalby were on target for the losers.
Broomhill set up a home semi-final against Oxenhope in the Division Three League Cup after seeing off Sutton 3-1. Joe Slater, Andrew Tanner and Simon Harris were their goalscorers.
Polonia Patson, second in Division Four, had a crushing 6-0 win at Barnoldswick Barons. Mirdslav Bak (2), Daniel Trojan (2), Stevem Brand and Karter Kryz were on target.
Goals from Chris Hoyle and Liam Wheeler enabled Bradley Reserves to edge out Pendle Renegades Reserves 2-1.
Ingrow & Worth Valley Reserves were on the wrong end of a 3-1 scoreline at Horton.
Goals from Carl Johnson, Danny Richardson and Don Sharp sealed the victory for Horton while Stuart Hoyle replied for Ingrow.