From my understanding, if an entity lends stock out it is still...

From my understanding, if an entity lends stock out it is still the beneficial owner (relevant interest) of that stock, and thus you would need to include any lent out stock in any substantial shareholder filings. If an entity is only acting as custodian and has no control over the stock, I would argue that the custodian does not have a relevant interest. If the custodian is lending out stock (possibly to borrowers shorting the stock), they would have a relevant interest. However, if a custodian does lend out stock, I would argue it should first gain the permission of the beneficial owner and/or the investment manager.

A lot of double counting takes place in substantial shareholder notices due to the concept of relevant interest. We saw it with Hancock prospecting and the family trust both submitting notices as they both had relevant interests in those shares.