Can I make fermented lemon soda using yogurt cultures?
Soda-like drinks have traditionally been made in the same way as beer, but with less fermentation to keep the alcohol content low. Without alcohol, (and with a bunch of protein and fat around from the yogurt) you run the risk of growing some botulism in your soda. Some traditional fermentation techniques carry risk of botulism, and any 'new' technique should undertaken very carefully. That being said, your soda should be quite acidic and probably safe. Get some pH paper and use it!

There are a few things I would change in this plan:

Yogurt is made at fairly high temperatures to encourage lactobacillus growth while inhibiting others. Find out the best temperature for your culture, and make sure you can maintain it during fermentation. 

Try get the culture growing independent of any yogurt: grow it in your sugar/lemon solution for a few generations without pressure and with a bit of oxygen. If it's still alive and still tastes good, you're probably OK. Otherwise, if the culture dies halfway through fermentation, something else is likely to grow in its place :-(

Lemon juice is quite acidic, and will clean metals quite nicely. So don't put your soda in any metal container unless your really like the taste of iron. (Even beer is acidic enough to cause this problem, fermentation is always in glass, plastic or stainless steel). Used plastic soda bottles work well when clean. 

The other major problem with a pressure cooker is getting the soda out: if the cooker did hold pressure from a fermentation (actually it will probably leak CO2 faster than it is made) you shouldn't be able to open it until the pressure is removed. Again, soda bottles are a good choice here.

Last - your water should not be chlorinated, the flavor of your soda could be ruined by chlorine.