Found your Sarah ~ TX Dth Idx Online: Sarah A. Perry d 7-18-75 in Bailey Co, TX ~ and on the SSDI: Sarah Perry b 18 Dec 1880, d Jul 1975, last residence Muleshoe, Bailey Co, TX and Soc. Sec # issued in TX.
Bailey Co, TX is right next to Lamb Co, TX.The TX Dth Idx Online doesn't begin until 1964, so can't look for William.If you know where he died, obtain his death certificate, and Sarah's, too.The names and birth location of their respective parents should be on their DCs.
Look at Bailey Co, TX GenWeb site, some GenWeb county sites are putting their cemeteries online.If you think William died somewhere else, and Sarah may have been taken back to the same cemetery, then check that county GenWeb site for possible cemetery records.
Once you find the name of William's father, you could check the 1870 census, when William would still be in the household of his parents.