The
best advice I can give is, "Get that cray out of the tank lest he be large enough to act upon his discovery that tetras sleep on the bottom. Darkness will not deter him; he's
built for hunting where visibility is poor."
That said, yes, crays do need a varied diet to stay healthy. They sometimes do catch live prey (like slow swimming fish, snoozing tetras, or goldies, which also sleep on the bottom), but for the most part, they are scavengers, and they are omnivores. Little dudes are growing fast, so keepers need to make sure that they are getting enough protein (in addition to greenery) and sufficient calcium to develop strong, healthy exoskeletons. As crays reach adult size, they don't need so much animal protein (still need some) and should get more vegetable matter. Most crayfish like pretty much any fish food pellet that sinks (shrimp pellets, algae wafers, spirulina pellets, etc.) and the Hikari Crab Cuisine as well. Tetra Repto-Min pellets will sink if you let them get a bit soft, then squish them up against the side of the tank, and those should be deemed acceptable by His Royal Crustacean-ness. They love frozen fish foods such as blood worms, brine shrimp, mysis shrimp and krill, but those should be used only as occasional treats rather than staples. I also like the Sally's frozen aquatic turtle diet; it's got anacharis (yes, the aquarium plant--crays love it), carrot, krill, romaine lettuce, turnip, pollock, dandelion greens, spirulina, the odd blood worm and a bunch of vitamins that I can't recall at the moment, and I'm too lazy to get up and go to the freezer. It's messy, but they like it. Peas are fine (so are most vegetables), and once in a while, you can offer a kernel of corn (as a treat, not every day; too much corn isn't good for them). ID loved the occasional bit of cantaloupe, and so do my crabs (red claws and hermies).
Crayfish are not difficult to feed; they aren't fussy and will eat practically anything (even chewing on soggy driftwood sometimes). As long as you offer a variety of foods and don't "lean" too far toward animal protein or vegetable matter, it'll be fine. He may also want to put in a small bit of cuttlebone (the stuff for birds), just in case Mr. Crusty wants a calcium snack. Don't put too much in at once, though; it will sink in time (or you can weight it), but if there's a big chunk left in the water too long, it stinks to high heaven. I cut it into little cubes about 1" (ish).
As long as we're on the topic of food and therefore digestion, healthy cray poo (yes, I'm making this a poo thread

) is firm and looks sort of like short, rectangular rods. No, I am not making that up--crab poo does, too. If it's stringy, or looks "mushy", he needs to hit the salad bar more often. That's important because you can't see the exo he is growing under the one he's wearing, so you won't know you haven't been feeding him right until the next time he moults. Moulting is hard on crays--it's the hardest thing they have to do and that's how I lost my beloved ID--so they need all the help they can get from their keepers to be in good condition for it.
As your friend is already discovering, crays are also professional escape artists. If there is a cray-sized hole in the lid, and any way to climb up to it, chances are pretty good that he will find it. If that happens, a good result is to find him doing a victory march across the living room floor, but if he's not found and put back in water before his gills dry out....not good. Plastic canvas makes a nice solution for cutouts around filters or heaters because it can be cut to an exact fit. Cut it a bit larger so it sits on top of the lid, then tape it down (I have black lids, so I use black duct tape). If you want to be really fancy and have time to let it cure, hold it in place with aquarium silicone.
In the event that no one has told your friend yet, (non-dwarf) crayfish are not plant-friendly. Some plants they eat, some they dig up, and some they just chop up for reasons known only to themselves. If it's a plant you don't want to risk losing, don't put it in a cray's tank because it might just happen.
Also worth noting is that it is normal for crays to be a bit lethargic/reclusive and lose their appetites right before they moult. After the moult, they'll take a breather and harden up a bit, then eat the old exoskeleton to reclaim the nutrients, so don't remove it. Don't handle newly moulted crayfish, and try not to touch them at all for a week after the moult.
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Everything's better with penguins.