TL;DR: Technically it's possible to acquire everything without paying a cent. It will just take a long time and a lot of work.
The Magic Keys you need to unlock lockboxes don't drop at all; the standard way to obtain them is by paying 125 Zen on the C-store.
Sometimes they're sold on the exchange by people who have money to burn and need the gold, but that's not a guarantee. However, if you're willing to put in a lot of work, you can get as much Zen as you need without ever paying a cent...
As user108818 tried to point out, there is a player-driven exchange market that lets you exchange "astral diamonds" (the refined kind, mind) for Zen (the PWE C-store currency) or vice versa.
The exchange rate is player-driven and fluctuates strongly depending on what people are willing to pay.
You earn "unrefined astral diamonds" through various forms of regular play, and can convert them to "refined astral diamonds" at a set limit per day (which is why there's a buyer's market for astral diamonds as well).
As of the current writing, and assuming the PC and XBOX versions have the same account, the exchange rate seems to be roughly 480-500 astral diamonds for one point of Zen.