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!
For longer term storage, there are many self storage units around the metro area. Not cheap, but then neither is paying extra baggage fees and lugging around extra stuff not needed for another leg of your trip, as it sounds like Terry might be doing. For example, I found "Downtown Denver Self Storage" with units starting at $45 a month. http://www.downtowndenverstorage.com/
The Operator (including employees, agents, and/or contractors of the Operator, the event and the venue) and/or law enforcement officials may access lockers and the locker facility at any and all times and may examine any items, even if such items are in a sealed bag, backpack, suitcase or the like. Any items which may cause a risk and/or nuisance to the Operator, other users, the storage facility, the venue or the event may be removed and destroyed without notice to user and at the user’s expense. User waives any right of privacy to item stored in the lockers.
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Wilderness Exchange is within walking distance of Union and they require you leave a bag with them when you go into the store, they may be willing to stash your bag for a few hours. No guarantee on that, but an option if you can't find anything else. They are only open 10am-6pm on Sundays, so you may have to wait around a bit or pick it up early depending on when you get there and will be leaving.
Laundry lockers are used in places like hospitals and food-processing workplaces where uniforms have to be collected, laundered, then returned to their owners. The locker cabinet contains a number of very narrow lockers, each of whose doors is keyed using a key held by the owner, so that they have access only to their own locker; but the entire array of doors is embedded in a much larger door covering the entire front of the cabinet. Opening this opens all the lockers simultaneously, and requires the use of a master key which is held by whoever collects items deposited in lockers, for laundering, then returned in the same way, after which they items are accessible to owners using their individual small doors.
With the same standard features as the Traditional line, the Traditional Plus Collection is intended for more rugged applications. Available in single-, double- or triple-tier configurations, this collection features 14 gauge doors with 16 gauge full-height reinforcement channels, frame-secured 11 gauge frame hooks with protruding padlock hasps, and a maintenance-free, single-point latching system.