Dickson, on-loan from Charlton until December, bagged a double on his debut in the club's 3-1 victory at Brentford on Saturday.
The Pirates have won six of their opening eight league matches and Lescott, who claimed his second goal of the season at Griffin Park, is hoping Dickson's long-term future lies with Paul Trollope's in-form side.
"Dicko got two and did really well. Saturday was his first game for us but he looked like he'd already been at the club for a while," Lescott told the Bristol Evening Post.
"Hopefully he can continue what he did for us at Brentford and we can keep him longer than his initial three months.
"He gives us a different dimension with his strength and his pace and we are fortunate now in that we've got four strikers at the club who have all got completely different attributes."