Is it true that the best ores are found near lava in Minecraft?

This is an urban legend and the reason it exists is this:

Lava spawns in all caverns just below the level that diamond spawns. Since opening up a cavern (where lava is) reveals a lot more blocks than just mining one block, people have come to believe that it's lava that causes ores to spawn, whereas it's really just you being able to see more blocks, which means you're bound to see more ores.

Not always, no. You can find any ore anywhere so long as you're at the right height for it. It just so happens that the level where lava spawns is also the level where diamonds do.
Nonetheless, you can find diamonds that aren't near lava.