The problem is that Lapper sets the next race restart time when you have confimed results in either a race OR a qual ssession. It doesn't check whether the current session is a qual or race. Most race servers will only do race rotations, not quals.
if you have the source code, you could modify the file to restart only if its a race session.
Replace the line in managePacket.cs:
<?php
...
void managePacket(InSim.Decoder.RES res) // RESult (qualify or confirmed finish)
{
if (newCfg.varsLapper.AutoRestartRaceSec > 0 && ( currRace.autoRestartOn == false || newCfg.varsLapper.AutoRestartOnFirstFinished == false ))
?>
<?php
...
void managePacket(InSim.Decoder.RES res) // RESult (qualify or confirmed finish)
{
if (newCfg.varsLapper.AutoRestartRaceSec > 0 && currRace.qualMins == 0 && ( currRace.autoRestartOn == false || newCfg.varsLapper.AutoRestartOnFirstFinished == false ))
?>