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Yet the Champions Cup is an elusive prize for Bath.
It has been almost 30 years since they last won the trophy, back in 1998 - when it was then the Heineken Cup - and another 20 years since they last reached this stage, the 2006 semi-final which they lost to Biarritz.
Memories of the all-conquering Bath side that dominated English rugby in the 1990s loom but, as Lawrence said, this is a side that wants to create its own legacy.
"The biggest thing that Johann talks to us [about] as a team, as a club, is we're trying to create our own history, but it all starts with one game at a time," Lawrence said.
"We go back to zero each week, we never think about what's going to be happening months down the line and at the start of the season we wanted to do well in this competition - but that started with that very first pre-season game against Munster.
"Of course we'd like to create our own legacy, do well in this competition, but the main thing is making sure each and every one of us go out there at the weekend and give the best version of ourselves."

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