@MichaelTrotochaud - My council appears to allow Lions to register as soon the the pre-K school year (or what would have been the pre-K school year had they attended pre-K) concludes. I’ve registered Lions before August 1 of the year the begin kindergarten with paper applications and had no trouble.
I’ve seen inconsistent information about the August 1 date, and it is possible this is a legacy from the August 1, 2018 official launch of the Lion program. Clearly, before that date, Lions was a pilot program. It may be that the August 1 date is still hanging around from that.
As @DanPare noted above, he was able to register his son a a Lion in May.