Reports leading up to the final day of the Premier League window suggested that the Brazilian was refusing to train with the Blues as he pushed for a late summer switch.
He got his wish as an £8 million ($10m) transfer was made across London on Thursday.
Lampard has now been quizzed on how that agreement came to pass and insists the decision to part ways was amicable and not forced by either side.
Explaining his decision to offload Luiz, the Blues manager said: “We had some conversations over the last week, honest ones, and the conclusion was that he should move on.
“It’s a position that I have a lot of competition. Everyone has to understand that.
“He has moved on and we wish him the absolute best, because he has been a big part of our history.
“There wasn’t any strike. No fall-outs, just honest conversations.
“As a player I want that as a manager, and I think I got that from David. Him not training was a decision I made as I felt that was best at the time.”
Lampard is not expecting there to be any further outgoings at Stamford Bridge with the window now closed for clubs in the top two tiers of English football.
He added: “I don’t expect there to be. We will see over the next few weeks.”
Chelsea are not in a position to bring anyone else into their squad, as they work under the constraints of a two-window transfer ban, and Lampard continues to try and see the positives in that.
He added on being forced to watch on as rivals scrambled around to get bodies on board before the deadline: “It is what it is. We have to remain competitive while we are in this position.
“With the ban it has been easy to write off this squad, and I don’t write off this squad at all.
“I think that what is important is that you have a target within the group. What matters is how we approach things. We will see how we go.
“We will aim to win and of course we want to be in the Champions League every year. We are realistic and we just have to work our hardest.
“Yes, [it is bridgeable] because this is football. One of the beauties is that you start again fresh.”
Chelsea are set to open a new era under Lampard’s guidance on Sunday when they kick off their 2019-20 campaign with a trip to Manchester United.