You'll probably find a more coherent look at the high end lenses vs the cheaper stuff. So for Canon, L glass will have a more coherent look given the better overall qualities, contrast, colour etc. If you shoot with a 35L and a 85L the look will match more vs the cheaper equivalents. Does it have a "look" over say high end Nikon glass? Don't know. Leica and Zeiss used to have a "signature" but even that is now diluted given the divergence and myriad of lenses and series. Look at Zeiss, the 35/50/85 had a look but now there's 3 fast 50s and so on. I think overall they are all going for the uber-sharp, clinical with obliterating bokeh look, basically bland rendering that caters for the pixel peepers. I suppose given the amount of image manipulation happening in post processing they might as well do that as any "character" will be gone.
Saying that, character for me is things like microcontrast, vignetting, in/out of focus transition and background rendering. Lenses that I have/had with a distinctive look would be the ZF 50/1.4, Summicron 50 and Nikon 50/1.2.