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.
Sloping tops: while most lockers have flat tops, some manufacturers offer the option of sloping tops to their range of lockers. The slope may be of either 30 degrees or 45 degrees to the horizontal, sloping towards the front, and the purpose of this is to make it impossible to store items on top of the lockers, or to make it harder for dust or other debris to accumulate there. This is an important factor in places like food-processing factories or restaurants where hygiene requirements must be met.
There are a number of features or characteristics which may vary in lockers. Because purchasers will need to specify what they want in each of these when ordering, it is more common to order a particular configuration rather than buy "off the shelf" in a shop, although certain very common configurations can be found in shops fairly easily. These features include:
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Tiers: may be specified as single-tier (full height), two-tier, three-tier, etc., meaning that the lockers are stacked on top of each other in layers two high, three high, etc. Tiers are commonly up to eight high; on occasion, even more tiers may be found, in the case of very small lockers for such purposes as storing laptop computers. The most common numbers of tiers found in lockers are, in order, one, two, and four; three-tier lockers are rather less common, and other numbers such as five, six, or eight even less common still - seven almost non-existent. Since locker cabinets are most commonly 6 feet (182.9 cm.) high (although there are exceptions), the height of individual lockers varies according to how many tiers are accommodated within the cabinet. The height of individual lockers is usually approximately 6 feet (182.9 cm.) divided by the number of tiers, so that two-tier lockers are about 3 feet (91.4 cm.) high, three-tier lockers 2 feet (61 cm.) high, four-tier lockers 1.5 feet (45.7 cm.) high, and so on. Standard features often vary according to the number of tiers: single-tier lockers usually include a shelf about a foot (roughly 30 cm.) from the top, and a hanging rail (sometimes with one or two hooks) immediately underneath that, at the top of the large compartment beneath the shelf; two- or three-tier lockers usually lack the shelf, but include the hanging rail; lockers with four or more tiers usually have none of these fittings, but consist of just the bare compartment.