Why isn't TTL metering accurate when using a non-electronic lens?

I recently bought a Lensbaby lens and I played with it a lot. Then lens is awesome but I have one big and annoying problem and is that TTL metering fails miserably when using P, TV and M modes.

I mean, the picture that the live view shows you is completely different that the one that gets recorded in the SD card.

The only mode where the camera meters correctly is in AV, but due to is a semi-automatic mode I have a lot of trouble trying to get the correct shutter speed (I deal with the AE-Lock button but it's very hard to get the number that I specifically want)

So, my question is why TTL metering is lost (or gets inaccurate) when using analog lenses (or the ones that don't have any electronic connection with the camera)? What extra information an electronic lens gives to the camera to meter correctly? Why the light coming through the lens isn't enough information in order to meter correctly?

Why my camera (Canon 550D) meters correctly in AV mode but not in M mode? How do you deal with it?

I tried using different metering modes, but still no luck. For example, I had to spend 5 to 10 minutes locking the exposure pointing to different light sources in order to get a 1/15 shutter speed and take this picture:

Setting the camera with that value in TV or M modes showed me a very underexposed image in LV mode. (Which made composition almost impossible)

Answer

The way TTL works is to measure the exposure of the scene when the aperture of the lens is wide open, and then when the picture is taken, it stops down to the correct aperture.

With a manual lens, oftentimes you have manually stopped the lens down already to the aperture you want, or because that is where the exposure reading is telling you it is correct. The camera however, because it has no data for the lens, is thinking that this is the reading of the aperture at it's widest setting (which it can only guess the value of unless you have a chip on your adaptor lens to tell it the aperture). So when you take the picture, the TTL and camera are confused because they don't know what the widest aperture represents, or even if the widest is being used for the photo.

I think the reason Av works is because with no other lens details available, the camera assumes that the aperture you are metering at is the same one you are taking the picture at, so makes no complicated compensations and the picture is taken as is.