Is it safe to use a disposable microwave-safe lunch box to cook raw rice with hot water directly in a microwave for 15 minutes?
It very much depends on the type of plastic,the thickness, and the manufacturing process. I highly recommend that if it's not . It's best to just learn about the company and see if they are FDA/ISO/ASTM approved or just some cheap Chinese company (nothing against Chinese things, however, there are good things made there too).

Here's a simple test that can be done: Put the box in the microwave, put a mug with water in the box, and microwave it for 30 seconds. If the box is warm, it probably isn't microwave safe (ESPECIALLY if the water is not). If the box is cool and the water is hot, you should be good. I can't provide a proof that this will work 100% of the time, however.

But may I also urge you to switch to glass? It'll save you money, it'll spread less plastic on our planet, and it feels better too.