It was a frustrating start for both sides, with LR taking advantage of Town's inability to deal with the overloaded balls in the penalty area, but also struggling to break a strong Ashton defense in the final third, with Ryan Talbot as frontman in attack.
LR kept their attacking tempo high, with Joe Bacon flying past Adam Morris on the left to launch balls into the box, but strong defensive work from Ben Lappin and Leon Wright denied the hosts.
After a goalless first half, the second started at a similar pace, with LR launching forward balls in an attempt to find a breakthrough.
It was the home side who broke the deadlock after a late challenge on Luke Nicholls on the edge of the penalty area. Kyle Robinson-Murray stepped up and smashed his shot into the corner of the net, giving LR the lead
As the end neared, the sloppy Town side tried hard to find an equalizer, which they almost did when a high ball found Burey, who found himself one-on-one, but a tempting three-point save from LR newcomer Jack McGovern denied the visitors an equalizer.
But LR's defensive luck would eventually run out after a struggle in the penalty area, where a ball was cleared off the line and bounced into the path of Kyle Preece, who scored in the 98th minute to send Town fans into a frenzy.
After the match, Lr boss Dave Jones felt it was more like two points lost than one won, but in reality a draw was a fair outcome.
He said: βIt probably feels that way [two points dropped] right at the end with the late goal, but if you asked anyone tonight they would agree that a point was probably a fair result.
“We are not going too low on that, we have also scored a few late ones ourselves, but I would like to thank Ashton Town for going all the way and deserving a point.”
LR travel to struggling Garstang next Saturday to continue their unbeaten form in the league (3pm).
They remain five points clear of second-placed Nelson at the top of the table.