If the y drive is not mapped or you have no rights to it it is a windows issue.

Check the log.nsf on the Y: drive to see if a local NSF file is reported as corrupt. If one is identified, run fixup (nfixup.exe in the Notes program directory) against the NSF. For example, if bookmark.nsf or names.nsf (the local Contacts) is reported as damaged, run nfixup against that file. Do this while not running Notes. If a repair fails, rename the file to something like bookmark-old.nsf after exiting Notes, and restart Notes. 

there is a simpler way to solve a problem similar to yours , you can use the service repair nsf file lotus notes. 

Why is there a space in the paths 'Y:\Lotus\Notes\ Data'' and ':\Programs file\lotus\notes\ notes.ini' ?

Are those really the paths used?  From the second path, the drive letter is missing and a directory name seems misspelled: 'programs file'.

Please note that having the data files on a networked location is not a recommended way of running the Notes client.