I haven't done L&G for a long time, so I don't recall if I took breaks, but I do take breaks in other workouts (like PLB or GS Legs) when I feel I need them, to recover for the next set and be able to do it with good form.
The reason could be the sequence of exercises, the use of some plyo moves in L&G (like the plyo lunges), the speed of exercises. Also, if by "Strong Legs"(?) you mean "Leaner Legs," that workout doesn't have step-ups, while L&G does, and those can really get your heart rate up and take your breath away. Whatever it is, listen to your body and you'll get better results and make improvements.