Probably not. There are a whole lot of Lees, most of them not related.
If you know of any direct-line male Lee relatives, you can try to get them to do a Y-DNA test to find out if they match any of the established twenty-five families at leedna.com http://leedna.com/dnaresults.php?sort=6 , or any of the ungrouped (there are a lot of them too).
They have a nice sortable chart, which makes it easier to figure things out.