ONLY IF,

The Private Pilot has let his/her medical lapse and intends to only operate in the future as a Light-Sport pilot.
 
Short answer - yes, if they are using an aircraft for which the CFI may give instruction. For reference, I think it works like this -

"...61.415 d - (d) You may not endorse a: ... (4) Logbook of a pilot for a flight review, unless you have conducted a review of that pilot in accordance with the requirements of ?61.56...."

"...? 61.193 Flight instructor privileges. ... A person who holds a flight instructor certificate is authorized within the limitations of that person's flight instructor certificate and ratings to train and issue endorsements that are required for: ... (g) A flight review, operating privilege, or recency of experience requirement of this part...."

"...? 61.56 Flight review. ... (c) Except as provided in paragraphs (d), (e), and (g) of this section, no person may act as pilot in command of an aircraft unless, since the beginning of the 24th calendar month before the month in which that pilot acts as pilot in command, that person has?... (1) Accomplished a flight review given in an aircraft for which that pilot is rated by an authorized instructor ... "

For example -

ATP shows up to take flight review in a cub. CFI gives endorsement - I think it counts even though he almost never flies a cub and spends almost all time in transport category aircraft.

Similarly, Private Pilot shows up with a Jabiru that is either SLSA or ELSA. Instructor is CFI - Sport Pilot. I think the review counts. If Private Pilot then goes out and gets a third class medical and begins flying TBM 850 at 40,000 feet it doesn't change that the flight review still counts.

I think that what doesn't count, at least for the present, is logging sport pilot time toward meeting the requirements for a higher certificate or rating.

Dan
 
I could be wrong here but one of my good friend is a CFI-S and he was able to give BFR for PPL up to last year or so. Accourding to him, he no longer can do that.
 
The Private Pilot has let his/her medical lapse and intends to only operate in the future as a Light-Sport pilot.

Not sure that's correct. As a Pvt / ASEL and Gilder, I can get a BFR from a CFI-G, so long as we do it in a glider. Since I am leagally authorized to operate an LSA with my PPL, I would assume that a CFI-S can give it to me if we do it in an LSA.

Similarly, if I'm a C / AMEL and fly jets, I can get a BFR from an A / SEL-only instructor if we use a single engine airplane. But then I'm still legal to go fly the jet again.

Unless Sport / LSA is different.