The people you are inviting already know why you waited until now for the Welcome Lucy party, so I don't think the timing is bad. Plus with the nice weather we're having, it's probably a lot easier to have the party now rather than the horrible weather we had in March and April. Hopefully September will be just as nice.
Anyway, I suggest you go as simple as possible. Depending on how formal your friends and family are, you could either send Save the Date cards or an E-vite (which is much easier).
A buffet is often simplest but provides a good variety of choices for your guests. Veggies and dip, chips and salsa, pasta salad, fruit, main course (sandwich tray, meatballs, etc.) and cupcakes, brownies or assorted pick up desserts. There are so many good recipe sites online where you can find some interesting recipes -- healthy versions, different flavors, etc.
Assuming there will be other children, you might want to get some activities for them. If you have outside space, get the punch balloons for the kids to bat around -- keep off the ground. Sidewalk chalk, bubbles, jump rope (depending on age), water guns if its hot. An age appropriate craft. Usually if the kids are happy then the adults are more relaxed.
Maybe minimal decorations. Cut out a star and let Tommy decorate it -- "today Lucy is the star" or something like that. Or you could do a group of stars, one for each of you, so Tommy doesn't feel left out.
Music in the background keeps the mood light.
As for the Godparent roles your sister and friend will be taking on, you could toast them and either call them Godparents (which actually has a religious background) or you could call them something like Alternates, or something else -- serious sounding or amusing, depending on your taste. Doing so introduces the role to your other family and friends.
My two cents on allowing your daughter to choose her religion when she's older. While we were raised Catholic, none of us, including my mother, married a Catholic. So a specific denomination has never been important. However, my sister decided to allow her daughter to choose whether or not she wanted religion in her life. With very minimal exposure, my niece (now 26) has chosen to have no religion or spirituality in her life. You could liken it to showing an adult a whole array of foods from which to choose. If only one dish is even remotely familiar, that will be the dish the person will choose. So, don't be surprised if your daughter chooses no religion. That may be fine with you, and I'm not judging. Just sharing an experience.
Have a wonderful time, whatever you choose.
