Can I retrieve a video from my lost iPad?

If you had iCloud Photos turned on in the iPad before you lost it, you can use any internet browser and go to www.icloud.com and go to the Photos app there. See: Set up and use iCloud Photos - Apple Support

If you didn't have iCloud Photos turned on but do have a backup to either iCloud or to a computer you can restore the backup to another iPad or use it to set up a new iPad. See: Restore your iPhone, iPad, or iPod touch from a backup - Apple Support

If you lost your device, you can view your photos and videos from iCloud on iCloud Photos.

When you are in iCloud Photos, click Library in the sidebar to see thumbnails of all your photos and videos. From there you can select your video you want.

View your photos and videos on iCloud.com - Apple Support