Maybe she should take that as a literal meaning that she has no SON but instead a daughter?
Would that set off Mordred's self-hating misogyny, or would the basic acknowledgement of her by Artoria as her child be enough to completely rewire Mordred's gender values and she'd suddenly flip to trying tirelessly to be as girly as possible? Mordred Lily unlock?
Thought this might be Misaki from Cross x Family in Koinaka Plus (the little bowtie in particular is similar to the one she wears as part of her waitress uniform), but we're missing an identifying mole on the chin here.