Every time you lay a mine, boost away, and the mine will detonate and disable the L ship's shields and turrets. As soon as all the turrets are gone, get one or two M transporters loaded with marines for about 500k each and board it. The L ship will go hostiles when your boarding pods land but it's got no more turrets to shoot you back and the L ship is easily yours, no reputation loss

From the basic Argon start, you can get your first L ship in as little as 2 hours!