I find on the 1870 Union Parish, Ward 1, Louisisana Census
Elasarus Smith Age:71 Born: abt 1799 Place of Birth: Georgia
Eliza Smith Age:67 Born: abt 1803 Place of Birth: Georgia
From BLM GLO Records I can see that Lazarus Smith owned property in Union Parish.This is Elasarus and Eliza are probably the same as in the 1860 Census you refer to and also the 1860 Lowndes County, Alabama Census where it shows daughter Lydia Smith.
I have tried to find a cemetery in Union Parish area where Elazarus/Lasarus and wife Eliza would be buried but have had no such luck.
I do note that the name Slawson is on the 1870 Union Parish, Ward 1, Louisiana Census so I think that is the spelling of the name, but that is only a guess.
Still can't prove anything about Lilley/Liddy and Lydia being the same person.Sure wish all registered with some one or I could find a marriage record, death or birth or newspaper article.I have gone to the Louisiana GenWeb and find nothing on John Gray family or Lazuras Smith family.
I go so long without a hint and then I get one which only asks more questions and I find really no answer of proof.Well just thought I would let you know about this 1870 Census for Elazarus and Eliza Smith.