"or are there any other ways to search the hard dive for the file" --> Yes, there are.
First look into your litterbasket, maybe the file is there.
Secondly look out for files with the same name but with strange or missing extension. Linux doesn't need the file extension an it could have been lost while saving.
As Flimm already stated, the .lnk files normally don't contain any content, but only information about the location of the original file. But it could have happend somehow, that the originl file has got erroneously the extension .lnk, so check for the filesize of these. Normal .lnk files are quite small, whereas your word file is probably somehow bigger. If so, rename it so word can open it again.
Thirdly do a search without specifying filename or extension but give some distinctive phrases or words from the text of your file (search file contents)
Be aware, that linux may have produced a backup copy of your file extended by a tilde (swung dash), which are normally invisible in some filemanagers. Activate view of hidden files and look for a file of the expected name ending with a tilde.
Finally: Use an internet serarch engine with the terms file recovery, which shows you a bunch of programs which will hopefully quarry your missing file. Avoid any saving and writing to your harddisk before using the programs. The less you write, the better are your chances to recover the file in case it has been deleted.
Not to forget: you will not find the file if you changed its permissions accidently. So be aware to perform your search with permisson to read files of all users (including root) on your system.
Look for unmounted drives. Your file could be stored there and will be only acessable when mounting the drive.