The Welshman has featured from the substitutes bench in the side's last two league outings after missing almost a full year through injury.
Speaking to the media ahead of tomorrow afternoon's trip to Perth to face St. Johnstone, the midfielder commented: "I'm not far off. Match fitness is completely different to training every day.
"Obviously I had a few behind closed doors games which helped me with my fitness, and I'm not too far off. Hopefully if I get a chance, I can show that I'm back to my old self.
"Hopefully I can have a massive [impact]. It's not just me, rather it's the whole collective. I'll try and do my bit for the team, as well as every other player in the dressing room.
"The manager has been great with me. He's always kept me in his plans and told me what he thinks.
"I had a really positive start, qualifying for the Champions League and we were playing well. It was hard because there were different stages to the injury. You need to look short-term rather than long-term. It was the little aims which you had to look forward to which kept me going.
"He watched me play as a young kid for Manchester United growing up, so he knows my game really well. When you're injured, you're obviously to the side a bit, but to know you have the manager's backing is great."
Tomorrow's visit to McDiarmid Park marks a return to league action for the Light Blues following the international hiatus.
Lawrence says the Gers are looking forward to the forthcoming block of matches and has challenged the dressing room to rise to the expectations of the Rangers support.
He continued: "It's been a difficult [start to the season], but we're looking forward now as opposed to the past. We need to look at tomorrow's game and that's all we can do. We have a good few weeks coming up, tough games, but it's what we enjoy doing.
"If you get that shirt on a matchday, you need to deliver. We have a big squad now, so every time that you're on the pitch you need to deliver for the team.
"We have a lot of new faces here. Playing for this club has big pressures, but you need to deliver. The fans deserve that and that's what we'll look to do.
"If you don't like pressure then this isn't the club for you. You need to thrive off that pressure. Having been a year out, I've missed that so much. You can't find that anywhere else apart from getting on the pitch, so I can't wait to getting back doing it week in, week out.
"We're trying to look forward. We need to have honest conversations with ourselves in the dressing room, and that's what we have done. We're going to come out of this and look forward."