Lunt was a big success on loan at Leeds last season and fancied a longer stay after playing in the Rhinos' 26-18 Grand Final win over Warrington in October. However, he was recalled by Huddersfield to fulfil the rest of his three-year contract and marked his return with a hat-trick of tries in Sunday's 36-12 pre-season friendly win over Widnes.
"I said I would have liked to have stayed at Leeds but sometimes in life you don't get what you want," he said. "I've been back at Huddersfield doing all the pre-season with the boys and I've really enjoyed it. I'm a lot happier with how I've been treated."
He added: "I lost my spot and you just want to play rugby at the end of the day. I had a great year at Leeds but, instead of dwelling on the past, I'm just looking forward to the season with the Giants."
Lunt, 25, won England honours after breaking through into Super League in 2009 but fell down the pecking order at the Giants last season. He lost the number nine jersey to Luke Robinson and also found himself behind Scott Moore and David Faiumu.
That has all now changed under Paul Anderson, with Robinson reverting to scrum-half, although Lunt insists he did not seek any guarantees from the new head coach.
"I got the nine shirt back which I'm really pleased about but I'm not a player who wants guarantees about playing every week," he said.
"I reckon if a coach says 'if you're fit, you're in the team', that's when you can take your eye off the ball a little bit.
"I just wanted to know that, if I'm playing well and doing the business on the pitch, then I'll get picked the week after.
"That's the only reassurance I want and he's given me that so I'm very happy."