Yes L-glutamine is absolutely essential, but usually something else is needed.
Adequate zinc is essential for all growth and healing and especially in the case of to cells with a rapid turnover, like in the gut. Research has shown that zinc deficiency is one of the most common things in people with leaky gut syndrome.
You need about 50-80mg zinc per day (definitely not more than 100mg, as at that point zince changes from being a benefit the immune system, to haveing a negative effect. It's as good idea to also take 1mg of copper per 20 mg zinc, since zinc supplements deplete copper.
Another essential is the amino Sugar
N-Acetyl-Glucosamine, which causes the secretion of the mucus that protects the guts cells, without this protection they will continue to get damaged.
Clinical trials have shown that a combination of these three is effective in clearing up leaky gut syndrome in about 8 weeks.