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Chelsea boss Tuchel has been lauded for the dramatic turnaround in results he has overseen at Stamford Bridge since his January appointment.
His side will compete for FA Cup and Champions League glory against Leicester City and Manchester City this month and are in control of their own destiny in the race for a top-four finish.
Tuchel, though, was not shy in recognising the contribution made by his predecessor and fan favourite Lampard in making those opportunities for silverware possible.
"Frank had an amazing record in the group stage of the Champions League," said Tuchel, who received a good luck message from the Englishman early in his tenure but has not been in contact since.
"He won all the FA Cup games. He's laid the foundation to get us to finals and we don't feel ashamed or have any fear to speak it out loud.
"It felt like that on the first day. I am aware Frank created his own legacy as a player and made it bigger as a coach.
"We stepped in halfway through the season and tried to fulfil the job he had began.
"Frank resembles everything you think about Chelsea. You think about Frank Lampard, the way he is, how he played football.
"This shows his character and the message he sent was a pleasure to receive. We had a message a couple of days after we arrived but nothing more."
After coming from behind to defeat Manchester City for the second time in three weeks on Saturday, Chelsea now have another huge domestic clash against London rivals Arsenal on Wednesday.
Chelsea is third in the table going into that game at Stamford Bridge – five points clear of West Ham in fifth – but the Gunners are not in the hunt, as they sit ninth having also gone out of the Europa League.
Tuchel sympathised with under-pressure Arsenal boss Mikel Arteta but insisted the Gunners – who face missing out on Europe for the first time since their 1995-96 absence - remain one of the top clubs on the continent.
Chelsea go into the match as favourites and are unbeaten in their last eight home Premier League matches against Arsenal, with six wins.
"I know what I go through when we don't win: it's the most horrible situation in the whole world, no matter if you coach in the academy or professional football," said Tuchel.
"That doesn't change during the week and it's the same for everybody.
"We are fully focused on ourselves and it's not for me to comment on Arsenal's situation, but nothing surprises me about this league, you can catch a streak or get caught in any match.
"That is what we signed up for: the toughest competition in Europe.
"Arsenal are one of the biggest clubs in Europe and we will prepare for our best level."
Mateo Kovacic and Andreas Christensen are out for Chelsea, but both have a chance of playing in the upcoming finals after a positive injury update from Tuchel.
The former Paris Saint-Germain head coach is expected to rotate his squad amid a gruelling run of fixtures, but he will not prioritise one match over another.
"We have an eye on the players' workload and the statistics we have, who is overloaded and from that we will decide who has a risk of injury," Tuchel said.
"Everyone who isn't a risk will be available for the game, it is not a case of managing for the [FA Cup final] on Saturday – we are in the middle of a [top-four] race."
Arsenal won 3-1 against Chelsea on Boxing Day earlier this season and have the chance to do a league double over the Blues for the first time since their Invincibles season ended in 2004.
But Chelsea has taken more points (22) from Premier League London derby games this season than any other side, winning seven of nine, with that Arsenal loss their lone defeat in such matches.