What are the chances of someone randomly browsing through an old union periodical finding a tidbit for your perusal on the same day that you post your query?
From March 1935 issue of Locomotive Engineers Journal, periodical of Brotherhood of Locomotive Engineers, Page 231.The wives of members had their counterpart support organization with initials G.I.A. (can't recall what that stands for at moment - brain fade), and said ladies' (referred to as "Sisters") organization disbursed and listed insurance claims each month for covered members:
"Sherman, Texas, June 1, 1934, [died] of heart trouble, Sister Emma L. LILLIS of Div. 396, aged 68 years.Carried two certificates dated June 1911, payable to Etta and Joseph Edward LILLIS, children."
So, Etta & Joseph's father was a locomotive engineer, probably on one of the many railroads that traversed the country surrounding Sherman, unless he had moved there after retirement.Their mother, Emma, was covered by two death benefit policies, each being a beneficiary.It cannot be determined from the listing if Emmas's husband was yet alive or deceased.
Note - I am not a LILLIS researcher - just supplying odds & ends in hopes that someone can use as leads in their "rooting".