I have a world that I created - survival world, no cheats enabled etc before I signed up for Realms. I imported this world into realms and it is my only Realm.
Playing the original solo copy on Xbox thunderstorms occur with expected normal frequency.
On the imported realm version, there has never been a single thunderstorm - 40+ hours (real time) and not a single thunderstorm. I have tried to stay for 10 to 15 Minecraft days in a various thunderstorm eligible biomes - plains, deep ocean, mountains etc and nothing - only normal precipitation either rain or snow.
I have also tried for hours in each difficulty - peaceful, easy, normal, hard - no difference - none had any thunderstorms.
Since no cheats or anything are enabled, there is not much I can do - what I have tried is copying the world back down to a solo world, set it to creative, then changed the weather to thunderstorm to confirm that every biome I tested above actually got thunder and lightning - which they all do.
Ok additional testing reveals that thunderstorms ARE happening - but they are not happening everywhere. I'm not sure if it is 100% chunk based as it seems to be an issue effecting smaller areas than chunks but will try to explain:
Lets say we have a set of blocks in the following pattern where each letter represents about a four block square:
ABC
DEF
GHI
I can be standing anywhere in region E, and the sky will be gray but no precipitation or thunder/lightening.
Moving to ABCDFGH or I, and there WILL be precipitation (and thunder/lightning if it is a thunderstorm). Then moving back to E it may or may not start precipitation but will never start thunder/lightening (even if the adjacent blocks are thunderstorm)
Entering and leaving blocks denoted by E will frequently toggle the precipitation in block E.
Notes:
*this is in an ICE biome so all precipitation is snow.
*there are additional anomolies is nearby blocks - ie it snows INSIDE my house but only on a 4x4 area of blocks (always the same 4x4 area when its snowing outside). The area is definitely covered by several layers of non-transparent blocks.
As noted above, this occurs is several different biomes where I was waiting for thunderstorms - apparently if I had just moved a few blocks to the side I would have detected them.