Should I tell him the truth?

Over the past few years, I have found it hard to deal with past trauma, and so it has caused me to act out (I accept full responsibility for my actions and have changed as a person).

I used to lie as a defensive mechanism (big lies) and this impacted my past relationships but they never found out that what I said was lies.

I recently reached out to one of my exes and explained that I lied and why I did and they forgave me (I wasn’t seeking forgiveness and it would’ve totally acceptable if they didn’t forgive me). However my other ex doesn’t know, this ex has blocked on social media (but not other methods of contact) so I don’t want to bother him, however I do think he deserves to know the truth. What should I do? I don’t want to “harass” him by telling him, but I do want to do the right thing.