Here's a French genealogy page connecting LaVoie with 'de la Voye' from Rouen, Normandie in the early 1600's.
http://www.geocities.com/Heartland/Meadows/2443/
just run it through your favourite translator or google 'Rene de la Voye' and then have it translate the page automatically. It has certificates and such to show the various incarnations of the name over time.
And here's one of Pierre de la Voye, from La Rochelle. Interesting, because Rene de la Voye above also had La Rochelle connections in his parents.
http://www.geocities.com/lavoiep66/pierre1ehist.html
I also found a French gite, near Boulogne/Rouen/Lille called the Collier Voye. So all things are pointing the direction of a placename origin and Normandie, France.
Voie in French has the penultimate meaning of 'way' as in montrer la voie 'lead the way' or cherche sa voie 'to look for one's way' (in life). It also has the meaning of channel, as in par voie de presse 'through the press' or par voie de mer 'by sea' and also 'road' - voie à sens unique is a one-way street in France - and 'track' - a sign saying défense de traverser les voies means 'stay off the tracks'. And it's a helpful word if you're ever in a French hospital...you may get your medicines par voie intraveineuse or if you're scared of needles, request them par voie buccale (orally).
As a placename it would refer to someone who lived by a road, route or path. The Gite named Collier Voye is next to a footpath to the sea. For more information, I'd have your librarian request borrow from the main library sytem a reference volume on American surnames or perhaps some on French surnames/genealogy to cite as references.
HTH!
Devon