Assistant coach Robinson takes temporary charge for a second time when Giants - who parted company with Simon Woolford last Wednesday - face Castleford Tigers on Thursday.
He helped end a six-game losing run with a 29-6 win over Wakefield Trinity in his first match and the 36-year-old former England scrum-half wants to be considered for the vacancy.
Lawrence made his debut in 2007, shortly before Robinson first joined the club, and said: “I’ve known Robbo for a long time, pretty much since my career started. He was always a great player and is a very smart coach; he’s a student of the game and has got the respect of all the boys.
“He did a great job with the Under 19s when he was in charge of them and has been into coach before when Chris Thorman and him took over a few years back.
“He’s no stranger to being a coach and he’s on the field with us every day. The transition couldn’t have gone any smoother really.
“All the boys have Robbo’s back and hopefully we can perform well for him. I’d have full faith in Robbo should he get the job.”
The 30-year-old admitted last week’s events were “pretty crazy” after it was agreed Australian Woolford - who was supposed to leave at the end of the season - would depart immediately.
Lawrence said: “With the nature of the defeats, I didn’t think we were doing too bad.
“Normally, in the past, when coaches have been let go, the team’s not been performing for a while but we’d had our best start to the season for a long time.
“But it’s a results-based business. Since we’ve come back (from lockdown), we’ve not performed too bad in some games - losing out by one point to Leeds twice and Warrington - but that’s the nature of it sometimes. Obviously it’s above players’ heads where the decisions are made and they’ve obviously decided they want to go in a different direction. But over the two years, I feel Simon has taken it forward and definitely strengthened the squad with players he brought in.
“We’re in a great position now to compete and keep building. I messaged Simon to say thanks for everything and hopefully catch up before he leaves for home.”
Lawrence believes there will now be an alteration in style, already hinted at against Trinity.
“Robbo is a very attack-minded coach; he likes to move the ball about and I think the brand of rugby will show that,” he said.
“Hopefully we’ll play some stuff that the fans enjoy watching. But alongside that we also have to make sure we defend well so we can get set a platform for the half-backs Lee Gaskell and Aidan Sezer to chuck the ball about.”
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