No one named "Sport" shows up on the Rev War pension index, but not everyone who fought obtained a pension, they had to be needy to do so.
No one named "Sport" shows up on the 1790 census index, nor on the 1790 census list of surnames from "Survey of American Census Schedules" by E. Kay Kirkham.
William Sport does show up on the 1800 census Robeson Co, NC.
You might post a query on the Rev War forum, see if someone has access to the index of military records for the Rev War.We have White's multi-volume set down at our library, but I won't be going there for a couple of weeks.
Go up click on My GenForum, click on Wars, click on American Revolution.Post your query there regarding military record of your William Sport and the fact you've been told he served with Henry "Lighthorse Harry" Lee's Brigade (note, it is horse, not house.)