Choose your location, frame your subject and record your footage. Keep your camera static on the tripod for the entire shoot. In a panning time lapse, it is essential to have as wide a shot as possible, so zoom your lens all the way out. Capture as much footage as possible -- you'll speed up the footage, thus shortening the length of your footage drastically.
Open your Final Cut Pro software. Log your footage by naming the clips you recorded. Digitize the footage. Create a new sequence. Click the sequence tab and select "Settings." Make sure that your sequence is a 1280-by-720 pixel resolution. You recorded in 1080, not 720, but this is still necessary, as you'll be increasing the size of your recorded video and higher resolution will prevent the image from being distorted.
Drag your clip into the new sequence. Select all of the footage in the sequence. Right click the footage and select "Change Speed..." In the "Change Speed..." window, your speed will default o 100 percent. Change this to 500 percent. Adjust the speed to your preference. If the footage you took is very slow -- grass growing or paint drying -- increasing your footage to somewhere around 3,000 percent is reasonable.
Double-click the video layer of your time-lapsed footage in your Final Cut Pro sequence. Increase the scale as much as you can while still keeping your subjects in frame. The larger you zoom in (or blow up) your video, the more room you'll have to pan.
Select the video layer in your Final Cut Pro sequence. If you want to pan from left to right, drag your video in your canvas to the right until you get to the edge of the image. If you want to pan from right to left, drag your video left until the right edge of the video meets the right edge of the canvas.
Move the cursor in your sequence to the beginning of your video clip. Double-click your video layer. Under the "Motion" tab, create a key frame in the "Position" section.
Move the cursor in your sequence to the end of your video clip. Drag your video in the canvas until the opposite end of your video clip meets the opposite edge of your canvas. Return to the "Motion" tab. A new key frame at the end of your video clip should be created for you. Move the cursor in your sequence back to the beginning of your clip and test your panning time-lapse.