I agree with the suggestion about shipping your skis and boots, especially if you are not going to be using them after the Vail portion of your trip. Are you staying in LA for awhile or just making a connection there? If you are staying at a hotel in LA perhaps you could talk to them about having your equipment shipped there and stored as most hotels do have some sort of luggage storage facility. Hikers on the Appalachian Trail often ship supplies to US post offices that are in towns easily accessible to the trail so they don't have to carry everything with them. A lot will depend on your actual itinerary and whether you are stopping over in LA or just making a connection. You'll likely need to do some research and maybe think outside the box. I know it's always much nicer to ski on equipment you are used to but renting might end up being your best bet and the least hassle.
Now that you’ve scored yourself some Denver luggage storage, the next thing on the list is finding things to do and places to explore. If it’s a Monday, a lot of the amazing indoor attractions and restaurants will be closed, but there is still plenty to do on any day of the week! See a concert at the Red Rock Amphitheatre, marvel at the beauty of the Cathedral of the Immaculate Conception or take a hike in the famous Rocky Mountains. You won’t regret it!
There is a luggage storage service a short one minute walk from Union Station in downtown Denver - LUGDEN. You can make a reservation online - lugden.com, call - (303) 747-5600, or show up as a walk-in. They offer hourly, day, overnight and weekly bag storage. Great place to store your luggage if you're on a layover from Denver International Airport, or going to a concert, or headed to a Rockies game at Coors field and want to enjoy yourself without having to lug your bags around.