Summer signing Ings scored his second league goal of the season to edge Brendan Rodgers’ men ahead three minutes before the half time interval, only for Lukaku to level due to more sloppy defending in stoppage time.
Neither side could produce a winning goal after the break and the local rivals had to settle for a sixth draw in seven Merseyside meetings.
The point moves Everton up one place to sixth and Liverpool stay in 10th spot, but just a point further adrift on 12 points.
Both sides engaged in a frenetic opening to the game but the first opportunity didn’t arrive until the 26th minute when Philippe Coutinho lifted a return pass into the box for James Milner to run on to but his angled effort was saved at the front post by Tim Howard.
Everton then enjoyed a good spell with a Ross Barkley free-kick whipped into the area from a central position headed at goal by Steven Naismith but Simon Mignolet denied him with a brilliant one-handed save.
Two minutes later Mamadou Sakho blocked Gerard Deulofeu’s right-wing cross but the ball fell kindly to James McCarthy, whose low strike was well saved by Mignolet.
Liverpool took the lead in the 42nd minute when Ings was left unmarked to head in a Milner left-wing corner from close range.
But Everton equalised in stoppage time when Lukaku lashed a low strike into the bottom corner after Emre Can’s clearance from Deulofeu’s right-wing cross hit off Martin Skrtel and fell into his path.
Chances were few and far between after the interval with Barkley’s run and shot from 30 yards dropping inches wide on 66 minutes, before Lukaku hit a shot straight at Mignolet four minutes later.
Liverpool’s closest to a winner came on 72 minutes but Coutinho also hit his effort straight at Howard.
Grimsby are open to talking to Sol Campbell about their vacant managerial position.