All I've got is acess to the census index.
In 1930 the young Leroy was living in Harris Township, Johnston County with his family:
(Name, approximate birthdate, relation)
Lambert, Claude, abt 1892, Head
----, Maggie, abt 1892, Wife
----, Trixie, abt 1912, Daughter
----, Leroy, abt 1917, Son
----, J B, abt 1919, Son
----, Feada L, abt 1921, Daughter
----, Ruby, abt 1923, Daughter
----, John, abt 1926, Son
----, Georgene, abt 1929, Son
Claude was born in Texas, everyone else in Oklahoma.
The old Leroy was living in Red Oak Township, Latimer, OK withhis family:
Lambert, Leroy, abt 1888,, Mississippi, Head
Emly Lambert, abt 1889, Arkansas, Wife
Ray Lambert, abt 1911, Son
Nell M Lambert, abt 1921, Daughter
Bessie Lambert, abt 1925, Son
(All the kids born in OK)
There are 4 Russell Walkers in OK in 1930. None of them are in Johnston County. All of them are old enough to have sired a child by 1937, although the one in Sequoyah would have been just 16.
Russell Walker, Council Grove, Oklahoma, OK, abt 1918Son
Russell A Walker, Oklahoma City, Oklahoma, OK, abt 1912 Son
Russell H Walker, Pawhuska, Osage, OK abt 1908, Son
Russell L Walker, Hanson, Sequoyah, OK abt 1919,Son
If I was guessing, I'd guess the Johnston County Leroy was trifling with your grandmother, she got pregnant, he lit out for the hills, your grandmother married Russell or otherwise convinced him to sign on as the father. Much later, maybe on her deathbed, she told your mother who her real father was. Your mother told her family, and when she died they put the true name on her death certificate.
Again, that is only a guess. The Johston County Leroy is exactly the right age to trifle with women in 1937 and skedaddle when his seeds bore fruit, so to speak.
If th ebirth cert. has Russell's age at the time you might narrow it down.