Lightning network lock period is much smaller (no more that a few days, if I'm not mistaken) than that of which can be used in the schema. For example, 3 months locking on the output of broadcasted transaction should not bee too big period for heir to wait before getting full control over the bitcoins and, in the same time, this will not make owner to be online 24/7 or use watchtower. A manual check one time in a month should be enough in this case.
I know LN time lock generally far shorter. But what if Alice forget to re-new the transaction and Bob spend the coin as soon as time lock duration expired? With high transaction fees, Alice only have about 10 minutes attempting to cancel / double-spend Bob's transaction.