I don’t know of any preset option in LO, but you can accomplish the same result this way.
Open Tools → Options → General and check “Enable experimental (unstable) features”. Then go to Tools → Macros → Record Macro. Once you click on it, macro recording will start so make sure you do only what you want to be saved, that is clicking on View → Web Layout and nothing but this. After that click the button “Stop Recording”. Save the macro in My Macros → Standard under the name WebLayout for example.
Now go to Tools → Customize, click on Events tab and select LibreOffice in “Save In” box. In the events list select “New Document” and click on “Macro…” button. Now choose the macro you created under My Macros and click OK. Do the same for “Open Document” event. After you’ve finished with everything, click OK to exit Customize window.
The next time you create new or open existing document, view will automatically be set to Web Layout.