stingray
Line Up and Wait
You can argue all you want about 61.415, but 61.195(b)(1) still applies -- if you don't have ASE on your CFI, you aren't an "authorized instructor" for non-LS airplanes. If you don't believe me, ask the FAA.
This is what I got back from Gleim:
Dan,
Thank you for your question. This is a fairly common issue. According to 14 CFR Part 61.415, you can provide instruction in any aircraft you hold category/class privileges for. That would include a Cessna 150 given your example below. Also reference 14 CFR Part 61.313. When seeking airplane certification for the Sport certificate, applicants are not limited to LSA but rather to "a single-engine airplane." Again, your Cessna 150 is acceptable.
Can the student solo the 150, take the checkride in it, or fly it as PIC after being certified as a Sport pilot? No, but there is no preclusion, based on my reading of the regulations, that would prohibit training in it - either for the student (logging time) or the appropriately rated/experienced instructor with a sport pilot rating (providing instruction).
I hope this response is helpful to you. If I can offer any further assistance, please feel free to contact me.
Thank you, have a great day, and fly safely!
Eric Crump, CFII/AGI
Aviation Editor
Gleim Publications, Inc.
4201 NW 95th Blvd
Gainesville, FL 32604