I'm afraid I don't know for sure since I don't use Lightroom.  In general the answer is Yes – you can use several different image manipulation programs on one set of .jpg files.  In fact, Picasa allows you to right click on a picture and 'Open with' some other program.  So, for example, I use Fireworks when I need to do more to a picture than Picasa.  I can do that no problem.  Picasa will then see the results of my work with Fireworks.

I see that Lightroom does 'non-destructive' editing – which is the same that Picasa does. 

You would need to know how and when to save the changes from each program so they can be seen in the other.

Oh … wait, you said something else … “store .jpgs in Picasa …”  Please understand that pictures are *not* stored in Picasa.  They are stored simply in My Pictures, and Picasa works with them there.  Fireworks, and most likely Lightroom also work with the pictures in My Pictures.  One picture can be worked on by many programs.

Just try it.  Open a picture with Lightroom and fix what you want.  Now view that picture using Picasa.  Do you get what you expect?