This depends on your settings. It can be immediate ... in fact it can even be before you finish downlding a file.

If you're adding your own material for sharing, see How to Share Folders (click on link) But once you've added files, you 'might' need to go the LW Library window & press the Refresh button before LW accounts for it. It depends.

To share files you're downlding, there's different ways.
1. You can share partial downlds where people can downld portions of your & other peoples downlds or shared files by getting from more than one source which will speed up their downlding. ie: they downld portions or segments of the file. To allow this, go to LW's menu bar, Tools>Options>Uploads>Basic & tick the option for Allow Partial Sharing.

2. To share files immediately you've downlded them, go to Tools>Options>Sharing & tick the option for Share finished downlds.

3. By default, your downld folder called 'Shared' is a sharing folder. But these files are not shared immediately unless you press the Refresh button or restart LW. But this is not necessary if you tick the option in no. 2 above.