There is a lounge a Leeds but it's nothing special. Choose the airport which is most convenient for you and don't worry about the lounge. There is a direct train service from Leeds to Manchester Airport (with First Class or Standard Class) and it rakes about an hour (
https://www.tpexpress.co.uk/). To get to LBA from Leeds you need to take a taxi (about 20 mins) or the airport bus (
https://www.flyingtigerbus.co.uk/).