Currently the first version of my short story -the PDF- is available under the status of "general access." What does this exactly mean, that one and all can come and buy it regardless from how they got to the page?
Why yes, that is what it means!
You can find the answer at this Knowledge Base article. Here is a sub-set of the article to directly answer your question:
General Access opens your work to all the Lulu.com visitors. Your project is available through search and browse on Lulu. In order to assign a General Access level, your material must meet the following guidelines:
Note: Your project must meet the guidelines in the Membership Agreement.