I attempted this repair. It is not like some phones, where the lcd and digitizer are stuck together with strong adhesive tape. They are glued together. You may get them apart, but part of the lcd will come off with the digitizer. You will have replace both, preferably with an entire assembly. Beware!! A lot of companies will sell you an assembly, but it is just the two separate pieces that they have stuck together themselves.
You can buy the parts separately and stick them together with adhesive, but it doesn't end up looking like the original. The thin space left between the two may cause issues.