I have a monthly subscription for Lightroom. Do I need another subscription for photoshop express?
PS Express is a free mobile app and companion to Photoshop. You can download it from Google Play, Apple and MS Stores.
And what's about the Premium Edition? Could I use my Adobe ID from my Lightroom Subscription to use it with Premium?
Look at the chart below to see what's included in your Plan.
I'm pretty sure a Premium Mobile app is extra and paid to the store from which you download it.