Could [name_f]Millie[/name_f] honor [name_m]Martin[/name_m] and [name_f]Lillian[/name_f]? The M honors [name_m]Martin[/name_m], which starts with M. [name_f]Lillie[/name_f] and [name_f]Millie[/name_f] obviously both have Illie in them. Full name would be [name_f]Emilia[/name_f].
You have a great name and a great nickname. Considering that you are aiming to honor two people with one name, I think [name_f]Millie[/name_f] works well. It is not a derivative of either name, but both names are represented.