The quick answer to your question is that Breez is a Lightning wallet and will generate a new invoice every time you want to deposit. You do not need to worry about an address.

The long answer is there are no Bitcoin addresses on the Lightning network. Instead payment channels are used and balances are kept track in those channels. A Lightning invoice will contain all the node, routing, and payment hash information to put funds in a payment channel.

A Lightning wallet is really just a way to look at your funds in a payment channel. This is also why you cannot navigate the Lightning network on a blockchain like on Bitcoin.

So on the Bitcoin network you just see Bitcoin getting locked into a funding transaction with witness data. On Lightning maybe you decide to buy a gift card with these funds and your wallet balance is now zero. The payment channel closes and on Bitcoin you will then see the UTXO's of that funding transaction being spent. The only Bitcoin addresses you see are the address that funded the Lightning wallet and the address where the funds locked into that channel got sent.

Basically all Lightning is doing is allowing two or more parties to agree on a balance. It does this by using multi signature scripts on Bitcoins base layer. This is why things happen "off chain". The thing that is happening off chain is negotiation, but the Bitcoin stays totally secure on chain to keep everyone honest.