You can almost always leave your car in any blue lined parking space (permit or not) using the blue parking disc during working hours (if I remember right, that's 8am to 7pm weekdays and 9-5 on saturdays). The blue disc gives you usually 1.5 hours but if you keep going back and changing the time on it, then you can potentially keep it there for ever.
Same goes for the parking meters - you pay between 8am and 7pm instead - but overnight it's free.
One additional thing: I always left my car without bothering to do anything. Depending on where you live (how central), the wardens do zones over periods of time, so where I lived (sous-gare) once every 4 weeks I'd get a CHF40 fine. I just looked at it as CHF40/month for on-street parking.
Otherwise here's a
list of Lausanne car parks.