why might a lender want to securitize?

there is no single reason but one, or a combination of the following, might apply:
1- to access an alternative source of funds - if deposits, or credit lines, are scare or expensive, securitization of assets, particularly if the securitized assets achieve a higher credit rating than the lending institution itself, can be attractive way of financing the business. Moreover this type of funding can be "matched"- the funding can be for the same tenor as the asset.
2- to release capital - provided the transaction meets the accounting criteria for being off balance sheet, Then the lender will release Scare capital to form the basis for further lending transactions.
3- to improve the return on capital - as long as the income received from the securitization exceeds its costs, the reduction in capital use should ensure that the overall return on capital is enhanced, provided the capital released is used for other profitable transactions (or a capital reconstruction, such as a share buy back.)
4- to improve liquidity - by securitising longer-term assets, using a matched term, the balance sheet can be made more liquid than before.
5- to reduce exposure- exposure to an individual sector, specific types of customer or certain types of asset can be reduced by securitization. This can be an absolute decision to cap or reduce exposure to a category of lending or to create headroom for further transactions.