I would give this to the lbs. I had exactly the same problem with the same motor and he fitted two spacers and redid the tension on the lockring. Sorted. Lateral play means simply that there isn't a tense grip between the motor, the column of spacers/cogs, and the lockring, which can come from insufficient spacers, I've got about 4mm on mine.
Spacers and tools can cost a lot but my lbs charged me £2 all in and it took him about 90 seconds.