Susannah/Susan mean lily in Hebrew but the child was called Sarah Catherine. Notice that mother signed with her mark.
Matilda Ann (McFarland) Weir also used her mark for 1917 marriage and birth of daughter Martha in 1918.
One thing which may or may not throw some light on Lily is school registers. By the time she was born the Infants Register might have given an exact date or month and years (should at the very least probably show age in years & months). Second register when she got into older grades should also record similar details. Presuming she was originally Sarah Catherine and born 1912 then she might have started school c1916- before 1917 marriage. Even if she was entered as Lily it should show if she was called McFarland. PRONI do have a large collection of registers (listed in their e-catalogue).
Also, any trace of a baptism?