Currently, if you are using the brand new “Lightning Experience” look of Salesforce, not all the functionality available in Salesforce Classic is available in Lightning. This isn’t a bad thing, Lighting is new and alive, changing and growing based on the world today and the ideas and needs of the Salesforce Community. It is to be expected. Some of the basics though, they should be available, but sadly are not.
As of today, there is no way for admins/developers to access the Recycling Bin in Lightning. To retrieve records that have been deleted, they first need to switch back to Salesforce Classic, access the bin, restore their record(s), then switch back to Lightning again. Bleh!. Talk about a pain in the @$$. (More information on restoring your data here)
LUCKILY, there is already an idea on the IdeaExchange, to add the recycling bin to Lightning. Yep, awesome idea that would take away a huge hassle for Lightning users. If you are a Classic or Lightning user, please take the time to check out the idea to add the Recycling Bin to LEX by Johan Yu and Vote It Up!