How can I be sure the engine, etc of my leased 2014 RAV4 are NOT damaged? Oil change by NTB Friday 8/31/18 resulted in MAJOR oil lose by Sunday 9/2/18. They admitted they caused it by over-tightening and breaking the O ring. They towed it to their shop Sunday to be fixed. I will pick it up tomorrow Tuesday and ask a lot of questions. What are my options if damage was caused by them?
I don't think anyone here can answer legal questions with any sort of authority, but the type of damage you can expect, assuming you lost enough oil and you didn't hear anything expensive make a real loud noise, is spun rod bearings, which basically means the engine would have to be disassembled completely and new bearings and possibly a new crankshaft would have to be fitted. And because the entire engine has to be taken apart, you're also looking at new head gaskets and possible a new timing belt. It's a lot of work and a lot of money.
But that's only IF (big IF) any damage was done. If the oil light on your dash didn't come on, there's no need to worry. And even if it did, it's not a done deal that there's major damage.
To answer your question whether or not there is damage, well, if the engine temperature didn't shoot up and there was no new, unpleasant sound from the engine, you're probably in luck.
In answer to the question; how can I be sure if the engine is damaged...
Short of disassembly and measuring of component parts against manufacturers specificaions and tolerances using a DTI gauge and micrometer, the most effective way to tell if an engine is healthy is to have a compression or leak down test carried out. That combined with a number of runs in various conditions to look at performance and heat loss characteristics and finally an emissions test and OBD scan for fault codes is probably the best way you can ascertain an engines health or otherwise.
Like I say, a full strip-down is the only way to be absolutely certain but if they're claiming that the engine is healthy and they're a Toyota recognised repair centre, that would probably be fairly excessive. I suppose you could tell a fair amount by just removing the sump and cam cover.
Something less invasive than a complete disassembly is to have an oil analysis done. You probably want to run the new oil for a week or two (assuming there aren't loud, alarming noises), Find a oil analysis vendor near you and follow their instructions for getting a sample. This can tell you if there is metal (and which kind) is in your oil as well as coolant, etc. You're looking for the results of damage.