Grosjean earned a one race ban last season after a Belgian Grand Prix collision that put Ferrari's title contender Fernando Alonso out of the race, with the Spaniard lucky to escape serious injury.
Red Bull's Australian Mark Webber dubbed the Frenchman a "first lap nutcase" for the number of starting crashes he was involved in but Grosjean has been addressing the problem since September with the help of a sports psychologist.
"He's a different guy," Lotus chairman Gerard Lopez told Reuters. "He knows what he has to do, he doesn't have that pressure, stress.
"We essentially have told him he's got a long-term future with us so now he can literally take it race by race, practice by practice. He's got the speed to win races so we think we've got a very good pair of drivers and a good car."
Lotus confirmed only in December that Grosjean, a former GP2 champion who is backed by team sponsor Total, would stay for a second season alongside Finland's 2007 world champion Kimi Raikkonen.
Raikkonen, who made his F1 comeback in 2012 after two years in rallying, won last season's Abu Dhabi Grand Prix and has set his sights on winning more than just a solitary race in 2013.
Lopez said that was a realistic aim.
"We feel pretty good about the car," he said. "We've got two drivers who now are really into it, know the team, know the car, know the tracks. I think Kimi would have won more races last year if it wasn't for a number of reasons."
Lotus are the only top team currently without a title sponsor, with rumours of a big deal in the pipeline failing to produce anything, but Lopez said that could change during the course of the season.
"We've had discussions and some of them were quite advanced," he said. "It's important to have the right package. and the right package is to a large extent also financial.
"I guess we could probably have signed a couple of things that leaked out but we think we are better off making sure that we sign what is the right thing for us.
"We will probably end up with something during the season," added the businessman. (Reporting by Alan Baldwin, editing by Patrick Johnston)