If we decide to lower the interest to keep a customer and it lowers the payment, should we disclose the LE with a CIC?

There is no regulatory requirement to do so and this would just be for informational purposes. However, if this loan is to be purchased by an investor there may be secondary market overlays.

I agree with Skittles. A reduced rate (and APR) in and of itself typically does not trigger a new LE. That said, if the rate was previously floating but now locked, a new LE would be required.

You have probably already thought of this, but if you have lowered your rate to keep a customer, you will want to make a good note of it for fair lending purposes (as well as review the impact of the practice on your fair lending posture).