At least in 1987, the Strada and Strada LX had some differences. Both lacked an integrated RD hanger (they were at the very bottom of Bianchi's road bike lineup), but the Strada LX had downtube shifter braze-ons and a chromoly fork, in contrast to the Strada's stem shifters and hi-ten fork. Due to the fork and a steel seatpost, the Strada weighed about a pound more.

What does the sticker on your fork say? It's looking more like you have a Strada LX, or that your year of Strada had the same spec as the 1987 LX.

Either way, I think you got a great deal. If built up with decent components it shouldn't end up too heavy, and will ride nice. In fact, the paint looks strong enough that I would reconsider painting it. A black frame can look pretty sharp once you've added the rest of the components.