My cousin Peter Lyddy did an extensive search about 20 years ago....I don't have his email, but will get it. He may have some insight. My understanding is that we went from LEDDY to LYDDY...and I think from the same part of Ireland. I will check with him and either he or I will be in touch. Our whole family is from the Bridgeport, CT area and I believe my great grandfather (and mother) came over in the late 1800s.
My best,
Anne Marie