Nope, LimeLM is designed to work with every publicly released version of TurboActivate. Occasionally an old version with emit bad data and we'll filter it (reject it) server-side. So, as a rule it's best to always use the latest version even if it's a "major" version.
And because all 4.x versions of TA, TF, TFS, etc. use TLS exclusively there will be a time in the future where old versions aren't compiled with enough "knowledge" of the newer TLS protocols and improvements. So eventually (likely decades down the line) old versions will be unable to contact the servers if you don't continue to use the latest versions we put out.
In short: no, we don't block old versions and we never will. However, you should *always* use the latest version (for bug fixes, security fixes, protocol improvements, and for features).