For governor running as a service, this was resolved long ago, and quotes added to the pathname. The theoretical exploit it could cause is very theoretical. On all NT6+ systems, a user would first have to get elevated rights to place a file in a location like "c:\program.exe", which would have to be a service executable, and if they had that right, they could also do just about anything else. So, it's severity 1 of 10, if that, but we did fix it.
Now, for the question asked:
As for the Task Scheduler, quoted paths are NOT used there. They aren't necessary because of the way the command is used by the Task Scheduler. You can check other system Tasks and you'll see the same.
For services, this is only necessary because they are backed by the registry, and due to the way they were originally implemented. That is something I will fix, but it's really not a serious issue, only a nit-picky one that has no real-world practical exploitation. Still I prefer to do things right, so will change this.
Attached is a screenshot showing Microsoft Office's Task Scheduler Action, which is not quoted, again because it's not necessary since the parameter is clearly defined as a whole entity, and treated as such by the Task Scheduler that launches it.
This is probably why when you place quotes there they are lost. That's not Process Lasso's doing, so much as the Task Scheduler's (though either could cause them to disappear as Lasso does recreate it's start entries during reinstall or auto-start config change).