I did this for about 13 weeks when I was already moderately strong (had just passed SFL before I did it) and it definitely made me stronger. I did it again when recovering from surgery and it got me back to strong quite well. So I think it can be a good choice but it matters quite a lot how you do it.... i.e. how closely you follow the program as written, how you pick your starting weights, how you advance the weight from one session to the next, how you handle misses/fails/bad days, whether you incorporate power cleans and chin-ups, whether you also do some type of cardio, whether you add anything besides that (not recommended)... If you have any questions I can help with I'd be happy to give you my thoughts. I haven't coached many people through the full LP but have been to the SS Seminar and have some practice coaching the lifts as they do. I think the overhead press every other session will be great for your goal of pressing the Beast!
I would recommend keeping your weight as steady as possible, just slowly increasing with a slight caloric surplus (maybe 500 kcal/day) as you build strength, keeping a close eye on your total protein (1.6g-2.0/kg/bodyweight/day). But I'm no dietary expert so take that FWIW, free forum advice.