In a small bowl, stir mayonnaise, chipotle, adobo sauce, salt, and pepper.
Place chicken in a medium heatproof bowl. Cover and microwave in 15-second increments, stirring between each, until warmed through, about 1 minute total.
Lay focaccia bottoms on a clean surface. Spread chipotle mayo over each slice; top with basil. Arrange chicken over each slice; season with pepper. Top each with mozzarella and tomato; generously season with salt and pepper. Top each with onion. Spread the rest of chipotle mayo onto each focaccia top and close sandwiches.
Heat a panini press or a large heavy pan over medium heat. Brush with oil. Working in batches if necessary, add sandwiches to panini press or pan; close press or top sandwich with another heavy pan.
Cook sandwiches until focaccia is crisp and golden brown on both sides and mozzarella is melted, 3 to 4 minutes. If toasting in a pan, cook until golden to brown and toasty on the bottom, 2 to 3 minutes, then remove top pan, flip sandwiches, and continue to cook until golden brown on top and mozzarella is melted, 1 to 2 minutes more.
Mix all of the ingredients for the lemonade.
Serve panini with chips, pickle, and homemade lemonade.