Klopp's men have been invited to participate in a light training session before and after Wednesday's game at the training ground in the Italian capital.
Lazio extended the same invitation to Manchester City when they faced Roma in the 2014 Champions League but this time, it was Lucas who facilitated the offer.
The 31-year-old moved to Liverpool in 2007 from Brazilian club Gremio and remained at Anfield for ten years before joining the Italian side last summer.