What angle should I set the VTA on my VPI turntable?

I go with Michael Fremer on this one. SRA 92 degrees as seen with a USB microscope. Otherwise set the arm so that the mounting surface of the cartridge is parallel to the surface of a 180 gram record. You will have to go pretty far ( over 3 degrees) one way or the other to make a difference in sound quality. It is not as critical as it is made out to be although I think people with more expensive line contact cartridges should try to be as accurate as possible. If they spend 10 grand on a cartridge they can plop $300 down on a USB microscope. 

My final settings are done by ear, using a couple of well-known (at least to me) records including the well known flying fish record about which there is an article for using that record to set VTA. There are other records as well: I first heard that Clements/Holland, Norman Blake and Tut Taylor record in a listening session decades ago, and Saurerkraut 'n Solar Energy was a killer then. 
But, using it to set VTA is for me, like a knife edge, and gets closer to the zone where you have to adjust for differences in sound, quicker. 
Once I'm dialed in, I don't change much- if it is a stupidly fat record, I'll take account of it, but I'm not down to adjusting per record. I also found that the need to do so varies by cartridge; that is, certain cartridges will sound better if dialed in more to whatever is happening in the grooves. 

9 out of 10 of us wouldn’t be able to measure SRA accurately even with a USB microscope. For most of us that method would be a waste of time and money, unless maybe one has been trained by an experienced person, like MF or Peter L. This has been shown more than once on various vinyl forums. IMO, the best advice is to set the top of the headshell parallel to the LP surface, then go up or down from there if the initial setting does not yield good tonal balance. As many others have already written.

what @lewm & @whart said!

IME, some carts demand frequent VTA adjustment to sound their best while others seem pretty damn happy and less sensitive to small adjustment. Cheers,
Spencer

bifwynne,
I see you upgraded to the VPI stainless arm with VTA adjust.  My experience with the original stainless unipivot is this: When VTA is changed, adjusting the tail up decreases VTF.  Adjusting it down increases VTF.  A lot.  If VTA isn't close, the adjuster won't make much difference in sound.  The fix was procedural.  I began using a VTA/VTF gridded block to level the cartridge and closed in on the VTA from there, readjusting VTA then VTF and repeating.  With the Lyra I imagine the situation is compounded by its' sensitivity to VTF.  You may have arrived back at the sweet spot of coil alignment but not SRA.  When in the ballpark, the range of the adjuster will take you from murky to shrill and finding the VTA sweet spot is easy.