Yes (again). For admin purposes, double check and make sure that the lender's interest isn't noted on the policy - if it is then you can have it removed or wait until maturity and the lender will need to confirm in writing to the insurer that they no longer have an interest in the policy.
Ensure that your relative has an up to date will, has considered any potential IHT liability, and has also considered what they would do in the event they needed to go into long term care as it appeaers from your post that they would have to self-fund.
Brian