Best distro for very old hardware ;) Runing very smoothly on 256MB is a miracle :)
Mint, LXLE and others does not work on old Thinkpads. Mine is a Thinkpad R50. Tried them "all". "Xubuntu 12.04 is the last of the family shipping with a non-PAE kernel. True, you can hack your way around, but from the official stand point, the vendor does not intend to support ancient processors beyond 2017." (ww.dedoimedo.com/computers/reviving-ten-year-old-laptop-linux.html) Most older distros are removed from downloads, no Xubuntu 12.04 anymore, also no torrent. Anyhow I succeded finding an Ubuntu 8.10 and it WORKS! Took hours to get there, upgrades are now pending.
I tried on my eMachine 355-M571G251lkk (double core CPU) with 1 G RAM, compared with Mint15 it was slightly faster but as soon as I opened more than one program, it showed obvious memory leak - the mouse cursor frozen or the drop-down menu clicked refused to show menu items apart from a grey box. Basically it is unusable so to speak. During installation, when the installation almost finished, the application frozen at 'copying installation logs'. I forced it to switch off. Is this the reason? I previously used Lubuntu without this problem. Later on I changed to Mint due to though Lubuntu a bit faster, it is apt to annoying problem like missing menu bar while Mint is more reliable and also fast enough.