I have an old PC with limited resources and I want to install Linux Mint on it but even Mate is too much for it. The only OS that runs smoothly on it is PClinuxOS openbox It's a lovely OS with good themes and splash screen and all but I prefer Mint. And my question is why can't we have an LXDE version of Mint??
You can There are various approaches to this. Some users have taken the Linux Mint 12 LXDE release, and upgraded that to Linux Mint 13. Others have taken Linux Mint 13 or 14, and just installed LXDE on top of that. You can do either. You could even remaster a Linux Mint ISO and replace its current desktop environment with LXDE.