I’d add one caveat. Building EAB allows you to deviate from the manufacturer’s kit instructions, so you could build an RV-12 EAB and make it ineligible as an LSA if say you put a constant speed prop on it or if you listed a gross weight higher than 1320 lbs on the AW certificate application. But I agree with Joe that as long as you don’t do something that takes it out of the definition of an LSA a sport pilot can fly it.
Wow, ok so this thread went a different way...
1. Yes, as RFSchaller inferred, E-AB and E-LSA can both be LSA. Compliance with LSA is defined in FAR 1.1 under Light-sport aircraft, which is:
[Light-sport aircraft means an aircraft, other than a helicopter or powered-lift that, since its original certification, has continued to meet the following:
(1) A maximum takeoff weight of not more than--
(i) 660 pounds (300 kilograms) for lighter-than-air aircraft;
(ii) 1,320 pounds (600 kilograms) for aircraft not intended for operation on water; or
(iii) 1,430 pounds (650 kilograms) for an aircraft intended for operation on water.
(2) A maximum airspeed in level flight with maximum continuous power (VH) of not more than 120 knots CAS under standard atmospheric conditions at sea level.
(3) A maximum never-exceed speed (VNE) of not more than 120 knots CAS for a glider.
(4) A maximum stalling speed or minimum steady flight speed without the use of lift-enhancing devices (VS1) of not more than 45 knots CAS at the aircraft's maximum certificated takeoff weight and most critical center of gravity.
(5) A maximum seating capacity of no more than two persons, including the pilot.
(6) A single, reciprocating engine, if powered.
(7) A fixed or ground-adjustable propeller if a powered aircraft other than a powered glider.
(8) A fixed or autofeathering propeller system if a powered glider.
(9) A fixed-pitch, semi-rigid, teetering, two-blade rotor system, if a gyroplane.
(10) A nonpressurized cabin, if equipped with a cabin.
(11) Fixed landing gear, except for an aircraft intended for operation on water or a glider.
(12) Fixed or repositionable landing gear, or a hull, for an aircraft intended for operation on water.
(13) Fixed or retractable landing gear for a glider. ]
2. I get what you're saying, but it's not really an E-AB issue, it's an LSA issue. Irrelavent of the certification, failure to comply with rules is non-compliant. It's even worse for E-LSA, because once you violate the LSA compliance, the airframe is done - it can't be recertificated. At least with E-AB, you can still keep flying the thing, just not as an LSA. You can deviate from any certificate - E-LSA, E-AB, or even a certified Part 23 aircraft for that matter, and violate the certificate. You're essentially stating that you need to follow the compliance rules to be in compliance with them. Ok, valid point.
3. The application you refer to is form FAA 8130-6, however note that there does not appear anywhere on the form a declared gross weight. I see this over and over - and cringe. The only statement of gross weight is the current weight and balance; and the application simply requires, in section VIII d. the FAA/Designee to ensure, "Current Weight and Balance Information Available in Aircraft". Legally, you could reissue a new W&B information to your aircraft 5 minutes after inspection. It seems silly to me doing that, but you could. The point being Gross Weight is simply on the W&B maintained in the airplane, not declared on the application.