With the
Emily,
Natalie,
Lincoln,
Asher, and
Henry set, the names are all fairly distinct from each other, which is nice. I probably wouldn't go with three of the names ending with an ee sound, so I would switch out
Natalie or
Emily for something ending with an L or A or a letter that hasn't already been used as an ending.
Lucy,
Alice,
Peter,
Milo, and
RobinOR
Gwendolyn,
Matilda,
Nicholas,
Roderick,
Jasper