This heavily depends on the number of open and new bugs. As far as I know, there is currently no date, because we have seen where this leads to.
To accelerate the process: Test, test, test LS 4 and report bugs.
I personally would estimate a couple of months, but the LS developer team is usually more "optimistic" than I am.
Disclaimer: I am not deeper involved in this and my assumptions are based on what I pick up from time to time between the lines in the developer meetings every Tuesday.
Help us to help you!
Provide your LS version and where it is installed (own server, uni/employer, SaaS hosting, etc.).
Always provide a LSS file (not LSQ or LSG).
Note: I answer at this forum in my spare time, I'm not a LimeSurvey GmbH employee.