How to improve the drainage of a patio with 6"x6"x39" cement blocks used for edging?
Drain holes aren't a practical solution here. If you insist on drilling them, you'll need a high powered impact drill with a concrete bit, then you either have to dig a trench on the outside to get the drill positioned parallel to the ground or pry up the concrete so you can drill above ground. At that point, you're still going to have a maintenance chore as those holes will clog up. In the winter, they may fill with water, freeze, and crack the concrete.

As such, I'd highly recommend just getting rid of the concrete. It's a poor design to begin with. Not sure what the original builder was thinking by putting that lip on it. Unless maybe the goal was to use it as an ice rink in the winter? :)

As it's not a monolithic slab of concrete, but in separate blocks/pieces, you may get away with just removing a couple piece at the low end of the patio to act as a funnel to allow the water to run off from that one spot. You may have to dig a dry well or something to accept that amount of concentrated water, though. I think it'd be better to remove them all instead.