For the majority of Amish churches the lunch served after services consists of a special mixed peanut butter we used to refer to as church peanut butter, bread, pickles, and peppermint tea. Those were the four staples though the option was there to also serve cheese, bologna, red beets, and cookies.
Some churches though do things a little differently. My Dad used to share how the church he grew up in served a hot bread and bean soup and apple schnitz half moon pie. Big bowls of soup were set on the table and everyone was given a spoon which they used to eat directly from the bowl.
Another church had the traditional peanut butter lunch, but afternoons they poured five gallon pails full of popcorn down the middle of the tables and everyone sat around snacking and visiting. The lady of the house would spend Saturday afternoon popping all that popcorn. Something I'm glad I never had to do.
The church we lived in when we chose to leave the Amish had a system where everyone took turns bringing something specific to church for lunch. The lady of the house provided the huge casseroles and coffee while the rest of the ladies arrived with salads, cakes, and desserts.
Somerset County Amish don't serve any type of lunch at church though they often invite other families home to enjoy a meal and an afternoon of visiting.