In a large skillet, heat 2 tablespoons olive oil over medium-high heat. Season the chicken with salt and pepper. Add to the skillet and cook, turning occasionally, until golden, 6 to 8 minutes; transfer to a plate. Let cool slightly before thinly slicing.
In the same skillet, heat 1 1/2 tablespoons olive oil over medium-high heat. Add the onions, season with salt and pepper and cook until golden, about 7 minutes. Stir in the pear and cook until tender, 3 to 5 minutes. Remove from the heat and toss with the chicken and cheese.
Divide the chicken mixture among the rolls. Using a panini press, cook the sandwiches according to the manufacturers instructions.
Meanwhile, in a large bowl, whisk together the lemon juice and remaining 1 1/2 tablespoons olive oil. Add the escarole and cucumber and toss; season with salt and pepper. Serve with the sandwiches.