LR almost forced a draw against Division One's form side Newcastle after a much-improved second-half display.
Newcastle looked strong before the break and took the lead on 35 minutes when Andy Bott converted a penalty after player-manager Nigel Gleghorn was fouled in the box.
Adam Beasley made it two shortly after the break, turning in a right-wing cross - but Atherton rallied to get themselves back in the game.
Jamie Cavanagh pulled a goal back on 68 minutes and almost snatched a second just before full time.
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