The 27-year-old has impressed during the past three race weekends, outqualifying team-mate Kimi Raikkonen twice and finishing on the podium in the German Grand Prix.
"With Romain, certainly over these last few races, he really has come on a huge amount and most of that is outside of the car," Permane told AUTOSPORT.
"He is noticeably more relaxed, more confident, happier out of the car. That translates to his driving."
Lotus team principal Eric Boullier backed Grosjean after an eventful Hungarian GP, in which Grosjean was twice hit with penalties.
Permane agrees that Grosjean's performance in Hungary and previous races has been very promising and is confident that the Frenchman can have a strong second half of the season.
"It's not just Hungary, Nurburgring as well," said Permane. "In the last two races he's done very well.
"He has performed well in and outs of the car and has been a bit of a different guy.
"I said to him after Nurburgring, 'I don't know what's going on but keep doing this'. He is working really well.
"He is calm, he is relaxed, he is not panicking about things and is qualifying and racing well.
"If he can keep that up, it really bodes well for the rest of the season."
GROSJEAN IN 2013
Start: 8th Finish: 10th
Struggles with a mystery car problem in the race, finishing an unspectacular 10th while team-mate Kimi Raikkonen wins.
Start: 11th Finish: 6th
Misses out on Q3, but turns in a strong race performance, beating his team-mate to sixth place.
Start: 6th Finish: 9th
Again complains about set-up problems and never shows convincing pace despite salvaging points.
Start: 11th Finish: 3rd
The victim of bad timing in qualifying as the track evolved rapidly, drives a superb race to pass Paul di Resta late on for third.
Start: 6th Finish: DNF
Is on target for a podium finish when a suspension problem forces him out of the race.
Start: 13th Finish: DNF
A dire weekend in which flashes of serious pace are tempered by accidents, culminating in rear-ending Daniel Ricciardo in the race.
Start: 22nd Finish: 13th
Qualifying is ruined by bad luck, meaning he is on a hiding to nothing in the race given the strategy chosen.
Start: 7th Finish: DNF
Outqualifies Raikkonen and matches him in the race, only to retire late on with front wing damage.
Start: 5th Finish: 3rd
Pushes Vettel for victory, but can't gain track position and slips behind Raikkonen in the final stint.
Start: 3rd Finish: 6th
A pre-race favourite, is hit with penalties for overtaking Felipe Massa outside of track limits and hitting Jenson Button.