Based on my experience over the past few years with Vienna Lager (9 batches bottled so far, one lagering right now), I have the following thoughts:
If you have a healthy pitch of yeast, you can leave the beer on the yeast once fermentation is done… popular wisdom these days is that you can leave the beer on the yeast for an additional 3 to 5 weeks without any negative effects. (I once did 7 weeks with the beer constantly below 55F with no noticeable negative effects) Essentially, if you start with healthy yeast and keep the yeast cool after fermentation, the yeast will last a long time before dying off and passing negative flavor compounds.
I personally, think my best lagers (and the BJCP judges tend to agree), are the ones that I leave on the yeast for a few extra weeks.
At the end of fermentation, the yeast tends to re-adsorb many of the flavor active compounds produced while multiplying. The more contact the yeast have with the beer, the more of these compounds can be adsorbed. One way to increase beer/yeast contact is what Budweiser does by tossing in steamed Beechwood chips during the aging process. This creates a lot of surface area for the yeast/beer contact and this greatly speeds up the “cleaning-up” process. However, by letting the beer sit in the carboy/bucket for an extra week or two, this accomplishes the same thing.
As for Filtering… I do not filter, but I would recommend waiting 6 weeks to filter, weather you leave the beer on the yeast or not, since filtering strips out the yeast from the beer, and much of the flavor change in lagers is due to yeast presence. However, in my opinion, after 6 weeks, the yeast are no longer doing much to help the beer and filtering them out will have no negative effects.
Hope that helps!