When you swap between bitcoin and Liquid bitcoin (LBTC) in the Blockstream app, the swap settles with transactions on two networks: one on the Bitcoin network and one on the Liquid Network. The swap completes once both transactions confirm, so the total time depends mostly on how quickly the Bitcoin transaction confirms.
For a Bitcoin transaction to finalize, a miner must include it in a block. New blocks arrive roughly every ten minutes, but there is a large amount of variance in that average, and an hour or more can pass without a new block. Block space is also limited, so miners prioritize the transactions with the highest fees. For more detail, see Why is my transaction taking so long to confirm?
The network fee you select with Change Speed when setting up the swap affects how quickly the Bitcoin side confirms. A slower speed costs less but can add significant waiting time when the network is busy.
The Liquid side of the swap is rarely the bottleneck. Liquid blocks are produced about every minute, and Liquid transactions are final after two confirmations, roughly two minutes.
Note: During a swap, funds first move to a temporary swap address which will not match the final recipient address. Once the swap completes, the swapped asset is delivered to your wallet, and you will see the transaction in your history.
A slow swap does not put your funds at risk. Your funds remain protected throughout the process, and if a swap cannot complete, the funds are returned to your wallet automatically. See Fix issues with on-chain swaps if your swap has not completed, or What to do if a wallet, transaction, or swap is not showing in the Blockstream app if you cannot find it.