The right search words will take you to the right places. For example, '40th Mississippi' will take you to this regimental history -
http://www.mississippiscv.org/MS_Units/40th_MS_INF.htm

Civil War Soldiers and Sailors shows W E Lee belonged to Co E, so we now know that Co E was called the "Steam Mill Rangers." We also know from the 40th Mississippi history that the regiment belonged to John C Moore's Brigade. I found General Moore's account of the Vcksburg Campaign using a search for 'Moore's Brigade' and 'Vicksburg' --
http://www.civilwarhome.com/moorevicksburgor.htm

There's a map showing Moore's Brigade in the center of the Vicksburg lines. Click on maps and select Vicksburg --
http://www.civilwar.org/maps/

The same search located this site on Confederate soldier mail from Vicksburg -
http://bellsouthpwp.net/p/a/parksvix/vixcwph.htm

It's more difficult to locate something about W. E. Lee. According the 1860 census of Kemper County MS, he was born in Georgia in 1843. Evidently Andrew J Lee brought his family there from Georgia between 1855 and 1860. W E Lee would have helped his father work on their farm. His service file shows that enlistment in Neshoba County MS, May 3, 1862. Lee died of wounds at Vicksburg on June 22, 1863.