Learn Italian: Avete comprato lo stesso identico vestito?

When placed before the noun, stesso means "the same" (indicating exact identity). If we put it after the noun, like il vestito stesso, it changes meaning to emphasize the noun itself, translating to "the dress itself."

Why do we use the article lo instead of il when vestito is a regular masculine noun?

The definite article always agrees with the word immediately following it, not just the core noun. Since stesso starts with an s + consonant, it requires lo. If stesso weren't there, it would just be il vestito.

Is identico necessary here, or is it just repeating stesso?

It is not strictly necessary, but it acts as an intensifier. Just like saying "the exact same" in English, lo stesso identico is a very common phrase in Italian to strongly emphasize that two things are absolutely identical.

Could I use medesimo in this sentence instead?

Yes, you could say il medesimo identico vestito, as medesimo also means "the same." However, stesso is much more natural for everyday conversations like this one. Notice that the article changes back to il because medesimo starts with a single consonant.