* Luckily, I remembered to bring my umbrella before leaving the house, as it started raining heavily just minutes later.
* The train was delayed, but luckily I had brought a book to read while I waited.
* The doctor said the surgery was a success, and luckily, my recovery is going smoothly.
* We lost our way in the woods, but luckily we found a trail that led us back to the car.
* I accidentally deleted my entire document, but luckily I had a backup.
Let me know if you'd like more examples or have a specific situation in mind!