Who is he and what has he done?
In the first "Jurassic Park", Alan Grant was a paleontologist who was hired by John Hammond to give his professional opinion about the park. Sadly, things took turn for the worst, and it caught Grant when he was with Tim and Lex at the tour car. the cinematic Donald Gennaro left them behind to save his hide, and Grant defended the kids from Rexy's territorial wrath.
Throughout the movie, Grant was Tim and Lex's parental figure, from guiding them to the assumed safety of the visitors center to shielding them from the raptors.
In "Jurassic Park 3", Dr. Continued his work as a paleontologist, but changed since the first movie. His JP3 incarnation was bitter, emotionally scarred from his encounter with the dinosaurs, obsessed with raptors and desperate enough to join Paul and Amanda Kirby's quest to Isla Sorna in exchange for a generous paycheck, taking his protegee Billy Brennan with him. Upon arriving on the island, Grant discovers that Paul and Amanda were dishonest. They were not wealthy or married, just middle class people who were searching for their son, Eric, who had gotten lost on the island eight weeks before. After the Kirbys realized Grant had never been on Isla Sorna, he was forced to lead the group, being the only person who has been on this experience. Grant, using his knowledge of dinosaurs, is the man who kept the Kirby family and his injured protegee alive, both as the responsible adult and by calling Ellie Sattler and informing her about the severe situation they were caught up in.
Why he doesn't qualify?
Grant is a noble man who always helped children and took responsibility, but there's one corrupting quality. The scene where he assaulted Paul Kirby unprovoked marks him as Lethal. I'm not defending Paul here. He did lie to Grant about the reasons to come to Isla Sorna, but PG heroes never assaulting people unless it's a last resort action. Grant had no justification to do so, and never shown remorse after doing so.
The final verdict
As a life-long JP enthusiastic, my bones are aching for saying it, but Grant should be cut. He's very close to be pure good, but his lethal moment (the category states that lethal heroes doesn't necessary kill people. They can also assault them without a really good and life threatening reason) prevent him from be considered as such.