Can you have someone in your family take the new DNA test (the oldest of Lacy descent in your family)?
I suspect we're related but can't find proof of all of Summers' children's names.
The DNA test would show if we're closely related.

I have some info on Summers, he was actually born in CT and moved to NY state, according to records, but there's always the possibility the family started out in VA. Or, maybe there was more than one Summers Lacy born about the same time.
Our own DNA test has matched many Lacy families from VA, as well as some in CT and some much further back, so I wondered if it was matching back before immigration.

The civil war wasn't until the 1860's, Summers Lacy was in western NY state (finger lakes region, just east of Niagara Falls area) by then, not down south. Could the story have gotten mixed up and have been Revolutionary War?

My own ancestor was Daniel Summers Lacy, born 1815 CT, both parents born in CT. I suspect Summers Lacy may have been his father or an uncle.
I also suspect I know Summers Lacy's ancestry, but haven't put it in a public tree as it's only conjecture and will be copied by others as fact.