Difference in temp is unbelievable

Lid thermometers are usually horrible. Stock ones that is. You can buy after market ones that are just fine. I don't even bother looking at mine anymore. I always just use the temp probe I have at grill level.

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My smoker thermometer is dead on.
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Yes, stock thermometers are rubbish, but you're not exactly comparing apples to apples.

Lid probe is measuring the air at the point the probe stops. The other one is on the cooking grill measuring the air around the meat. They are always going to give different readings, potentially significantly (i.e. if the meat is cold, it would push the temp of the second probe down).

The bizarre thing about your situation, is that the grill temp should almost always be higher than the lid.

Whilst most people just ignore the lid probe, I like to use it as well (even though I use a Tappecue) and also have another probe in the firebox of my offset.

But if you're going to do that, you need a quality probe like the Tel-Tru ones. There is a whole range of dial and stem sizes, temp ranges, even glow in the dark faces. They are much more expensive than the cheapo ones, but not that bad in the scheme of things. This one is under $30. 
They only start to get truly expensive when you start trying to get one that goes over 1000F (like the one I wanted for my firebox).

I've never used a maverick, but i suspect its similar to the Tappecue, and I can say that when I have done some testing, the Tel-Tru in my offset's cooking chamber lid, the tappecue probe sitting just above the cooking grate (on a little stand), and my Taylor Thermocouple thermometer all read "about" the same. I say "about" because its impossible to measure the same piece of air with 3 thermometers at once so some very minor variance is expected.