Plausible? May be? Kind a?
Probably not, but for fun........................
First weight:
You might have a hard time with the 900 lbs, but day vfr, wood prop, you might get there, but it would be a challenge. You can always limit the gross at sacrifice of fuel and payload. Of course with a light engine and prop you will have an aft CG issue with a passenger for sure. So plan on an extended engine mount or moving the wing back a few inches. Both not real practical.
Second performance:
Speed? Interesting? A 150 hp RV-4 is 201 mph. Now 100 HP would be
201 = X * (150 / 100 ) ^ 0.333 ; X = 175 mph (too fast)
You have 66.6 % if the power, but that does NOT lower your speed 33.3 %.
Speed and HP are approx on a cubed root.
Working backwards if you need 138 mph you would have:
201 = 138 * (150/X)^0.333 ; X = 48.5 HP!
Keep in mind a RV-9A with a 118 hp goes 173 mph so this above rough calc is not too far off.
The bad news is your climb rate with 49 hp, will be so low, say 300-400 fpm. Low drag is great for top speed but it is HP that gets you climb rate.
I would say the RV-4 would NOT make a good LSA because the design was made for +200 mph, +2000 fpm climb and 1500 lbs gross with 150-180 hp. However as a testament to how versatile of a design it is, it almost makes it as a LSA. Think of all the little cheap engines you could use in the 50 HP range. Hummmmmm Briggs and Stratton.
Does anyone remember the
DA-11, 125 mph cruise on 18 HP Briggs & Sratton?
http://www.aircraftspruce.com/da11.html
(
4 cycle engine, tricycle gear configuration with a steerable nose wheel. It is equipped with a 12V battery, starter, alternator, regulator, ammeter, key start, electric fuel pump, engine driven fuel pump....empty weight 175 lbs! gross 375 lbs!. Now you know why Van says keep it light. )
It would be a fun experiment to try to make a RV-4 a LSA. I suppose you could use a 100 hp engine and add drag, such as no wheel or gear fairings. This would give you better climb and help keep the speed below the magic 138 mph. You would still need to do more. The W&B issue would have to be addressed. One approach is a slightly longer engine mount and cowl. Also keep the tail of the plane (anything behind 1/3 wing chord) as light as possible, such as no paint and primer on back of the plane. Forget tail lights.
I can tell you a lot of ultralights go a little too fast and are a little too heavy, from what my ultralight acquaintances tell me. The FAA to their credit does not hide in the bushes, trying catching fast heavy ultralights. How could they, and they have better fish to fry.
Frankly I bet some of the "official" LSA's push the limits? Look, performance limits are hard to regulate. I guess there is an official LSA approval process? Don't they need some kind of official engine? A Rotax?
However the LSA is a little more official. I suppose there are going to be two types or classes of LSA's. One is the factory or OEM LSA's and the other the experimental LSA's. I suppose the oversight of experimental LSA's will be similar to any experimental. Can you the builder just declare a homebuilt a LSA? Do you need the FAA to bless and sanction your kit plane as a LSA? If that is the case, FAA blessing, than the whole topic of a RV being a LSA is academic.
In your hypothetical RV-4 LSA, you could limit the throttle to 2/3rds or over pitch the prop to keep the speed down. It is an interesting question. Would the FAA say OK to that? I will say the RV-4 as a LSA is slightly plausible but not practical.
If the FAA would let you keep the speed down with a throttle limit, you could turn many RV's into single seat LSA's! I doubt that will work and don't know the LSA regs. I am not sure this class of plane/pilot will be a big success but lets hope so.