I have my doubts. But, you might open a support ticket with the Limesurvey GmbH and ask them directly. They might be willing to get your Database dump and use it for your Limesurvey Pro account. Not sure if this is possible or not, but only they will be able to tell.
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.
If you self-host LS3, please write at support@limesurvey.org. Unfortunately, as mentioned above, there is no script available to easily "convert" LS4 databases to LS3.