This is a crucial point, especially since lying got you in this unwanted situation in the first place.
Make sure they know that you will make whatever changes necessary to prove that you won’t hurt them that way again, and that you are committed to working it out. Remind your partner that you are doing everything you can to build the trust back, and you will stop at nothing to make sure they never have to feel betrayed again.
Don’t be overly flattering or affectionate, as it might look like you’re just sucking up.
So you slipped and told a little white lie, and your partner caught you red-handed.
Now, you’re faced with the frustrating consequences of your actions, and your partner no longer trusts you.
Let them know that your actions will be sincere, and your words will be genuine from here on out, and your partner can hold you to that.