It is more than likely that when Martha was married to John W. Lewthwaite, her son William met Sarah Jane, because John W. and Sarah Jane were related somehow, but I don't know that John W. and Sarah Jane were father and daughter.
Ancestry.com is an expensive subscription. Folks who get it plan to use it alot. I would first suggest using it at your local library or LDS family history center first, to see if it is something you would get alot of use out of.You should be able to print copies of all of your grandfather's military paperwork.
I am starting to feel like John Devlin and Martha Sweeting are definitely your William's parents, and I would suggest getting their marriage record, to learn the name and occupation of John's father.
That marriage is: John Devlin married Martha Sweeting in the April-May-June quarter of 1887 in Middlesbrough (volume 9d, page 830).
I believe the certificates are £9.25 each. If you have an interest in knowing who Sarah Jane's father is, you could also get her marriage certificate. Sarah Jane Lewthwaite married Edward Cranmer in the April-May-June quarter of 1904 in Middlesbrough (volume 9d, page 1047).The volume and page number are needed in your order.