In short yes it has enough lift.
Whether you are of a 'large' build or not it is likely you will reduce the amount of lead you use over time anyway. New divers almost always reduce their lead requirements as they gain experience and relax, and then lose bad habits (such as finning upwards).
When you are correctly weighted what the BC needs to compensate for is the extra weight you are carrying at the start of the dive that you use up during the dive, in other words the weight of the air in your tanks, and anything that compresses during the dive such as neoprene.
So even if you are significantly overweight because you are carrying too much lead it will not be by 37 lbs because you do need at least some of this weight to compensate for your positive buoyancy.
If for example you only really need half of the weight you are currently using (in other words at 37 lbs you are very overweighted) then that is still only 18lbs, plus the weight of the air in your tank, another couple of pounds, and neoprene compression at the depths you are doing will not add too much more, so you are nowhere near approaching the capacity of the Zeagle Ranger at 44 lbs.
Best - Phil.