Nginx doesn't have permission to access files with the same ownership
Solution 1:
The nginx user is not able to traverse the filesystem to reach the folder where you have placed your site. A user must have the execute (+x) permission on a folder in order to be able to traverse it. From your permission information, drwx------ lamnk users lmank
shows that only the directory's owner has the right to read, write, and execute on the folder. Therefore, nginx cannot access that folder or any subfolders thereof unless it is run as that user.
You should grant execute rights on /home/lamnk with chmod og+x /home/lamnk
so that users other than yourself are allowed to traverse the folder. Without read rights, they still cannot list or read the contents of that folder, and without write rights they cannot make any changes to the contents; so there is no security risk to this, and it is necessary if you want to have subfolders of your home directory which are visible to other users, such as the nginx user. The mask you're looking to see on that folder would be drwx--x--x
.