No, you cannot edit the body or custom blocks directly in Layout Builder.* You can only edit the page layout by clicking the Layout tab. However, you can learn where you need to go to edit the content you wish to edit by clicking on the Layout Tab: Watch this video to learn how to use Layout Builder to determine how to get to the content you want to edit, or read on...
To edit a custom block: Go to Structure > Block Layout > Custom block library and find / select the custom block you would like to edit.
To edit the content in the body of a page: Click the "Edit" tab to edit your body content.
If you are in Layout Builder and you click on the pencil icon at the top right of the block, then "Configure", you will see the title of the block, or the category "Body" for the body block -- the pencil icon does not have an edit functionality in Layout Builder. The options are "Configure", "Move", and "Remove block".
* If you are able to edit a custom block in Layout Builder, it's an inline custom block, which you should avoid (see "Inline Custom Blocks").