Can I program OP_CHECKLOCKTIMEVERIFY to trigger based on external verifiable events? Can OP_CHECKLOCKTIMEVERIFY and multi-sig be used to trigger a transaction based on external verifiable events?

Some potential uses I have in mind:


Death
College graduation of a child or grandchild
Issuance of building permits
Yearly net company profits exceeding a certain threshold
Deposit refund after verification that vacation rental property is undamaged
Maybe not with OP_CHECKLOCKTIMEVERIFY, as it is not possible to consume an external input with that particular operation. But you can write a third-party oracle that will release some secret (i.e. a hash) based on the set of potential use-cases you have suggested, so the beneficiary could redeem the funds promised on the fulfillments of the condition.

A contract similar to that of a Hashed-Timelock Contract (HTLC) should be useful in this situation.