Give it some thought. What types of lubrication, what meter to select, metrics to collect, number of cycles... For the meter, if you used the free Harbor Freight, I don't think the one I tested made it 2000 cycles. But it was free. The 17B+ is about $130/ea. One for each test. Could easily wrap $1000 into it and a month of run time. Best to have some very clear goals in mind.
For the test to be useful, the only lubricants I'd think that would be worth considering are those that do
not inhibit conductivity between contacts, seeing how the idea is to preserve the full functionality of the meter. And, of course, the lubricant cannot itself be very conductive, if at all, since otherwise you'd almost certainly wind up creating conductive paths between selector tracks that were intended to be insulated from each other. Chances are that automatically puts you into special-purpose lubricant territory. It would be useful to test multiple brands and types of lubricants that meet the conductivity requirement.
For the meter, you'd want it to be something cheap. The idea is to test the effect of the lubricants relative to running the meter dry (and a cheap meter will almost certainly
not have lubricated contacts from the factory. You might make dry contacts from the factory a requirement of any meter being considered, unless you know what lubricant the factory is using (in which case one of the meters you'd test would be that meter with its lubricant removed).
It occurs to me that some meters will have gold plated contacts and others won't. So you might need to use two sets of meters, one with gold plated contacts and one without. If there are multiple plating options for the non-gold-plated contacts then I'd say whichever type tends to be the most common in the multimeter offerings is the one to use for the non-gold-plated option.
While I realize that there is likely to be a considerable difference in the contacts (e.g., with respect to the thickness of the plating) between a higher priced meter and a lower priced one, the idea here is to examine the effects of the lubricants. So I'm inclined to say whichever meter is cheapest and has gold plated contacts is the one to use for that option, and then for the non-gold-plated meter, you choose whichever one is cheapest and has the type of plating that is most commonly found across meter makes and models (as opposed to in the meter population itself, i.e. you ignore how many units of any given make and model are out there).
I haven't a clue what lubricants to consider for the test, other than that they can't inhibit conductivity or markedly increase it.
There are two different effects I think we'd want to see tested here. The first is, of course, the number of cycles of the selector switch that can be tolerated before failure. The second is to see how much of an effect, if any, the lubricant has on the accuracy and functionality of the meter. The latter might be something worth recording against number of cycles of the switch so you can see how the accuracy of the meter changes with switch use with the lubricant in question, and compare against how it changes when the contacts are not lubricated.
Anyway, should make for some interesting results.