i think i found your grandfather in the 1880 census for Philadelphia. his wife is shown as Mary and their son is Edward J Lawlar.As i am sure you have found that the spelling of the lalor/Lawlor/Lawler names are varied. Edward Sr worked in a woolen mill. He was 55 and Mary was 46, Edward jr was 17.
I found Francis in the 1930 census and he was living with Charles J Murphy and his wife Edith.he was 18.
Edith is shown in the 1910 census as a sister but i would guess she was from the first marriage as it is showing that edward and Amilia were married 9 years and had 2 children and that 1 survived.
other than showing that they were from ireland or Irish Free State there is nothing in the census that shows where they came from.