Cleckheaton’s fine eight-wicket win, coupled with a third straight defeat for champions Woodlands, saw John Wood’s men move to the summit.
Lawrence made a good start with Callam Goldthorp (67) and Adam Waite (51) making contributions before overseas man Ammar Mahmood claimed 5-34 as the home side were bowled out for 182.
Iain Wardlaw has missed several games due to his commitments with Yorkshire and Scotland but he returned and chipped in with 3-52.
The division’s leading run scorer Tim Jackson is in the best form of his career and he produced another fine innings of 84.
Captain Wood made 43 and Mahmood followed up his bowling efforts by also making an unbeaten 43 as Cleckheaton eased to victory.
Since key all-rounder Chris Brice suffered an arm injury, Woodlands have squandered a healthy lead at the top and defeat to Lightcliffe — the side who knocked the champions out of the Priestley Cup — saw them slip to second place.
Alex Stead (94) and Chris Taylor (64) who put on 154 for the second wicket, while Oliver Robinson made 58 not out as Lightcliffe set 253-5.
Simon Mason replied with five sixes and six fours in a superb knock of 102 but although Grant Soames (39) supported, Woodlands were bowled out for 213 as Robinson (4-51) and Suleman Khan (3-45) shone.
Hanging Heaton sent Baildon crashing to the foot of the table as they inflicted an eight-wicket defeat on the hosts.
Mark Lawson (5-29) and David Stiff (4-34) helped dismiss Baildon for 148 despite the efforts of Gharib Razak (45) and Vaibhav Naik (35).
Gary Fellows then led Heaton to an away win as the former Yorkshire batsman made an unbeaten 82 which contained one six and 11 fours.
Victory for Heaton, allowed Morley to leapfrog Baildon to second-bottom as they recorded a 62-run win over Manningham Mills.
East Bierley inflicted a 169-run thrashing on struggling Bradford & Bingley last Saturday.
Tabbi Bhatti (57), captain Kez Ahmed (53) and Gavin Hamilton (40) made useful runs to help Bierley reach 240, with Jack Hartley picking up 4-69.
Overseas paceman Waqas Maqsood claimed 4-23 in reply and Kez Ahmed picked up 4-12 as the Beest were dismissed for just 71.