You first have to close LR then Delete the .lock file.
Also post the exact path to where the catalog is stored. In Win/File Explorer find the folder the catalog is stored in and right click on it then select Properties. In the Security tab see if your username is listed and or Administrators and see what the permissions is set to.
You should also go to the Top Level folder in that path and check the permissions. By Top Level I mean if the path to that catalog is C:\Users\YourUserName\Pictures\Adobe\Adobe Lightroom\CatalogName you would go to your User Name folder or if you are brave the Users folder and check the permissions.
Personally I create a separate folder outside my UserName folder to store the LR catalog. And I add my User Name to the list in the security tab and give it Full Control.
If you deleted your catalog file (and don't have a backup) then you have lost your work. Did you look in the trash and see if it was there?
The .lock file does not cause this message. The message you got was about permissions, you need to have WRITE permission on the folder where the catalog file was stored. But if you deleted it, you had better get it back.
Sorry but I didn't read your whole first post.
As stated above you should never delete the catalog file. But you may be in luck. By default LR creates a backup of the catalog file once a week, unless you changed that setting or have been skipping it. So in the same folder the original catalog file was in there should be a folder called Backups. in there you should file other folders that have dates as their name and in those date folders a copy of your catalog. Select the newest date folder and COPY the catalog file and paste it into some other folder that you create on your hard drive.
Then double click that copied catalog file and LR should open with all your image files and all your work in tact.