Career
Youth career
Born in Aversa, Campania started his career at Arzano 99. He then left for Persicetana, a team located in San Giovanni in Persiceto, Emilia–Romagna region. He was selected to Emilia–Romagna regional Allievi team for the 2007 edition of 2007 Coppa Nazionale Primavera.
Palumbo left for Parma in 2007.
Cesena
In June 2011, Palumbo was swapped with Thomas Fabbri of A.C. (before Christ) Cesena. Both players was signed by co-ownership deal and valued the 50% registration rights for €1 million.
Both clubs had a selling profit of nearly €2 million, however the increase only in form of intangible asset (the contract value of TFabbri and LPalumbo) Both players signed a 4-year contract. L.Palumbo was loaned to Fondi for 2011-2012 season, rejoining Parma team-mate Loris Formuso, Andrea Gasparri, Abel Gigli, Domenico Iovinella and Daniele Bernasconi.
The loan of Palumbo was renewed for 2012-2013 season.
The club also signed Zsolt Tamási and Giuseppe Pacini from Parma. On 20 June 2013 Palumbo joined Cesena outright for €1.5 million, however still part of the mega swap deal. In July 2013 Palumbo moved to Arzanese.
On 31 January 2015 Palumbo and Felice Di Cecco were moved to Slovenian club North Dakota Gorica in temporary deals.