Yeah I only asked because I agree with the above poster that we can't consider WebP common yet but was unsure if I was forgetting something. I can see the utility in this then, at least as a stopgap.
I've researched lossy GIF too: http://pornel.net/lossygif but even lossy version wasn't better than PNG.
LZW is just a very poor compression. Even best case is taking ridiculous amount of bits (you can only add 1 byte to previously used pattern, so it's sequence of symbols for 1+2+3+5+6+etc. pixels resetting every 4k iterations), so there isn't even room for improvement.