Matching lighting

Is this what you're looking to try and do?

https://www.youtube.com/watch?v=MKVlSiVOaxk

I haven't found a way to do this in After Effects yet. I'm sure it's possible with expressions, though.

Hopefully, someone knows a good way of going about this in AE.

Automatically varying the brightness of the new plate (uniformly across the plate) is quite easy with expressions. Simply track a representative point on the existing plate, then use the sampleImage() expression to read the RGBA value of a small group of pixels under the track point. You can then use those time-varying RGB values to control brightness/tint adjustments on the new plate layer. It's not going to replicate partial shadows moving across the plate, but it's probably too small in frame to care about that.

A walk-through of a similar task (using sampleImage to set the brightness of a lens flare) is here.

Seeing the clip certainly would help. If it needs to be exact, you may need to reconstruct the shadows with elaborate masking based on the original clip - obviously - but otherwise this stuff can be faked pretty well using Fractal Noise scaled to large proportions and animating its offset and evolution. You may just need to find a good timing and random seed that halfway decently matches the pattern. and play around with blending modes and coloration.

Mylenium

You have two options, maybe 3. Go to Red Giant and take a look at the VFX Suite or Red Giant Complete. There are tools there that will automate the process for you. 

The other option is to work with additional layers, gradients, blend modes, and color correction tools to match the lighting. Depending on the shot, this could be 2 layers or 40. For example:

The basic plate is cut out of the background using Set Matte from a masked Solid called Matte 1, Then shape layers with multiple gradients are overlaid to light up the plate and a frame gradient was created from a combination of inside and outside mattes to overlay on the plate frame with a blend mode and transparency. The flow chart shows the effects used and you can see the blend modes in the animated gif. When you get the lighting matched up pre-compose and add the fixed plate to the shot. I honestly have had to use 40 or 50 layers to match the lighting in some scenes. Red Giant's compositing toolset makes this a lot easier, but you can do it by hand. I've been doing this kind of lighting matchups for more than 25 years. 

The flow chart for this sample   - took me about 15 minutes.