There's a TX death record for a Mrs M.F. LAMB with those dates that lists her parents as Z.R. BEASLY and Bell YOUNG.The informant on the death certificate was Mrs. Thomas FISHER.
I can find Z.R. (Zachariah) BEASLY and his second wife Eliza Jane NORWOOD, whom he married in 1877, in the 1900 and 1880 censuses, but none of the children living with them are of the correct age to be M.F.In 1880 the oldest child still at home is 13 and was born in TX, so they must have been there by 1867, but I haven't been able to find them in the 1870 census.Though I just a death record for son James who was born about 1868 and it says he was born in Kentucky.
There's a KY marriage record for Zachariah R. BEASLY to an Elmira YOUNG in Logan Co, KY in 1855.Groom's birthplace was Butler Co.
There's an application for a military headstone for Z.R. BEASLEY, b. 5-Mar-1830, d. 13-Sept-1902, buried Center Grove, Mt. Pleasant, TX.He was a private in Company A, 14th Texas Infantry, CSA.This is another indication that the family was in TX by the early 1860s.
The 1850 census for Butler Co, KY has this family: BEESLEY, Thomas age 51 b. VA Mary A. age 37 b. VA Zachariah age 20 Frances age 14 ALLEN, Jonathan age 30 ALLEN, Agnes age 24 ALLEN, Sarah age 2
Two households away is John BEESLEY, age 56 and Sarah are 52 both b. VA.
I'm sorry this isn't more helpful.I think the key to finding her name is the 1870 census and I searched it every way I know how.While this gives you something about her family, it doesn't tell you her name or Mr. Lamb's name or if she had any children.According to her death certificate she had only been in Bastrop for 2 days before she died.