From Civil War Data Systems:
William Lee 12 Aug 1861 to 25 Sept 1864 Pvt Co F 6 KS Cav
From Ancestry.com's Civil War pension index:
William O. Lee Co F 6 KS Cav
widow's pension applicated 519557 TX (1 June 1891)
Appearently William died about May 1891. His widow filed an application for pension, but the pension was never granted (no certificate issued).
I hope this helps.