The duo were Fartowners team-mates for four years before Connor made the switch to the Black and Whites at the end of 2016.
The talented back has gone on to win a Challenge Cup and England recognition but is also renowned for his on-field niggle.
Loose forward Lawrence, 29, said: “Jake? Jake is Jake.
“He’s the biggest wind-up merchant you’ll ever meet. He’s a great bloke but on the field he’s a master at getting under people’s skin.
“We knew what he was like all the way from when he came through the Academy. We know he’ll be trying to wind us all up at the weekend but we’ll be doing the same to him as well.
“It’s always good fun. I just laugh it off. He can’t really get under my skin but, with a few of the other boys, he really knows just how to push their buttons.”
While Hull are already in the top-five ahead of today’s game at Anfield, Huddersfield hope to soon join them having picked up a much-needed win over Hull KR last week.
That sees them up to ninth, four points off the pace, but Lawrence accepts they must find consistency if they are going to go the right way up the table.
“In the context of our year, it was a massive win for us,” he said.
“The story of our season so far – in the first half of the campaign – has been very inconsistent.
“We can play well for patches and then switch off for 20 minutes and it can cost us.
“We want to change that in the second half of the year and we need to.
“Hull are playing really well and have played some good rugby for the last eight weeks or so.
“It will be another big challenge on Saturday. They have talented players all over the field – not just Jake who has that X factor – but it’s one we’re looking forward to.
“We’ll have to improve again from last week and sort out our discipline; Hull will kill us if we give that many penalties away again. But if we get that and our defence in order we will go a long way.”