The problem isn't lmtp itself, it's that you're using -L parameter, which causes LMTP processes to open the log files directly.
Just to be sure, isn't this the only way to have a separate LMTP log files?
The only way to reopen the log files is to restart those LMTP processes. "doveadm reload" should do it.
Thanks, I will try this.
Best regards Henrik Larsson