Some tips, and information to check :
* What version and operation system, do you use, and are there any mods ?
* Does a file named SAVE.DAT exist in the directory of the executable ? Or maybe, is there another file, that seems to be a safegame.
* Is it write protected, has zero size or has other problems ?
* Do you have enough disk space, and write acess on the partition ? (Is it a CD-ROM, Floppy Disk, Network drive, or is your user account restricted)
* Did you properly install it ? Did you properly extract the files from the ZIP file, or just run the executable from the ZIP file ? (Normally, this shouldn't work at all, but maybe some drives allow read acess to the packed art files)
* If you have a Anti-Virus, check its log. Is there anything suspicious. (F.e. Did it mistake LCS for malware, or did some actual malware (Crypto-Ransomware) damage files)
* What do you mean with clicking the X Key?
** If you pressed X in the Safehouse-menu, you properly quitted and the game should be saved.
** If you clicked it instead, nothing should have happened (there is no mouse support)
** If you clicked the cross on Windows windows (assuming you are not using fullscreen), you killed the process. This means, you didn't safe this in-game day, but normally the game is autosaved everytime, you wait a day. Maybe, you have a version without autosave ? If this is the case, you should get a version with autosave, as this also helps with crashes.