Hi,
Thanks for the bin description, this afternoon the words DOG + KITCHEN BIN came to mind, they're crafty like that, I've seen them in action
, your description of bin and purpose(s) helps to understand the motivation.
One thing, the greased telescopic tube idea is the wrong way round: telescopic bit would have to go on lid, and receiver tube on bin body to work, and I suspect be inclined at a minute angle from the horizontal to slip out well, and only in one direction... Not a good design after all.
I think perhaps, based on the little I know and the double, inward-opening bin lid, that a push (outwards) solenoid via a circuit responding to the tilt switch could be a solution, as only when the bin is tipped over in any direction the circuit would trigger and the solenoid stick could lock in place to a latch, e.g. a suitable diameter (metal hoop or rigid plastic) fitted into a plastic housing, pre-designed in as part of the bin lid plastic moulding, the same space needed to fit the solenoid, with suitable plastic, not something that melts/goes gooey at low temperatures, if that can be visualised.
Maybe you could look at muscle-wire to hold the lids taut only when tipped, not sure how sturdy that would be, and would probably need to be outside the bin so I'd avoid that as it could be an electrical risk for animals (and humans obviously) if additional housing is not included to cover it fully and robustly.
I'll keep thinking of bad suggestions, if any more come to mind, what I would say is that a) this would use quite a lot of power, even if only on sporadically, and b) it raises the price of a bin considerably, unless you're manufacturing thousands of them. i.e. Normal cat flap: 15 GBP, microchip tagged pet cat flap (has a sensor, microcontoller type IC and a latch mechanism added): ~80GBP...
The benefit of the 17mm action push solenoid is (you can get them for about $15 - $18) that one should keep both a single and a double-lid type locked shut, plus the tilt switch, another $15 at least, then other parts, add maybe $10 - $20; plus (your) labour...$$$: that's a niche market or one-off labour of love device, marketable to people sick of tidying house and stains from carpets on returning home, maybe!! A passive, electricity-free version is perhaps worth racking brain over, if it exists.