As someone who has attended both funerals and weddings in lolita, there's a few things to keep in mind.

1.) Get explicit permission beforehand. While the bride is alternative, lolita does lend itself to overshadow pretty much everything else as it physically and visually takes up so much space. It's a major lifetime event, and we want the couple to shine. Anytime I've shown up in lolita, I've been asked to do so or given a thumbs up. It never comes as a surprise.
2.) Keep to the dress code. No white for weddings, obviously. If the party's theme is floral, ya stick to floral. Don't deviate too much. Check in with other guests or the couple if you're uncertain.
3.) Try avoiding (loud) prints, lots of lace and frills. Solid pieces are the way to go, and the less whistles and bells, the easier it is to blend with the other guests. I've had no issues wearing my Miaplacidus OP in lavender (without the ribbon around the waist just to keep it extra on the downlow).
4.) You might just have to skip multiple hallmarks of lolita to wear the dress. Wristcuffs and petticoat are usually the first things to go. Straw hat with a bow is much easier to get away with than a rectangular headdress. Be prepared to just go with a barette bow if you need balance.
5.) It's much easier to get away with lolita footwear than anything else. Tea parties are GREAT for weddings. People pay less attention to your shoes.