Denver International Airport is the closest to Lakewood, Colorado. The airport generally is easy to fly in/out of from the area - it's a huge airport, so expect that there will likely be a good amount of walking. Danielle and Christopher have travelled through here a ton, so don't hesitate to reach out if you have any questions.
If you're not renting a car and plan to travel from Denver International Airport up to the mountains - Keystone, Breckenridge, Vail, etc. - consider Epic Mountain Express. Epic Mountain Express offers shared and private transportation services: Shuttles, YourRIDE+ and Premier BLACK SUVs.