oof that’s what I’m afraid of! Thanks for your insight 
My favorite here by far is [name_f]Lydia[/name_f]. So beautiful and tragically underused. You didn’t mention anything about why you like it though so it sounds like you might lean toward the others more intuitively?
My favorite is [name_f]Lydia[/name_f]!
I think [name_f]Maddy[/name_f] is pretty tough to avoid, but [name_f]Kate[/name_f] and [name_f]Katie[/name_f] can be if other nicknames are already established.
I would go with [name_m]Mads[/name_m] not [name_f]Maddy[/name_f]. If you call your child by a certain name, others will follow. Same thing with [name_f]Katherine[/name_f]. I prefer [name_f]Madeline[/name_f].
My favourite is [name_f]Katherine[/name_f]/Catherine, though I do like all your names. If you choose [name_f]Katherine[/name_f] or [name_f]Madeline[/name_f] you just have to be prepared to correct people if they shorten it to something you don’t want. [name_m]Plenty[/name_m] of people do this (myself included when people automatically shorten my name to the usual nickname). Have your preferred short form ready to go, so if they say [name_f]Maddy[/name_f] you say ‘No, it’s [name_f]Madeline[/name_f] or [name_f]Mae[/name_f]’. [name_f]Mae[/name_f] is a great option. So is [name_u]Kit[/name_u] for [name_f]Katherine[/name_f].
All lovely names though. [name_f]Lydia[/name_f], as others have said, is the less used choice, and may have less nickname issues.
Another vote here for [name_f]Lydia[/name_f]! What a gorgeous, underused name. I think it’s unlikely to be nicknamed regularly, too. [name_f]Lydia[/name_f] [name_f]Katherine[/name_f] is stunning! I like [name_f]Lydia[/name_f] [name_f]Madeline[/name_f] too.
I don’t know whether or not this is realistic but my hunch is that [name_f]Madeline[/name_f] would stand a higher chance of being nicknamed [name_f]Maddy[/name_f] than [name_f]Katherine[/name_f] would of being nicknamed [name_f]Katie[/name_f]. I think that [name_f]Katherine[/name_f] has more well-established intuitive nicknames than [name_f]Madeline[/name_f] does, plus I know at least one [name_f]Katherine[/name_f] whom I’ve never heard called anything other than [name_f]Katherine[/name_f]. I don’t know any Madelines so I don’t know if it gets nicknamed automatically. Maybe you could make [name_f]Mina[/name_f] work as a nickname for [name_f]Madeline[/name_f]? [name_u]Or[/name_u] [name_f]Mimi[/name_f]?
All three are lovely names, you can’t really go wrong with any of them IMO 