Lička began his footballing career at Czech club Baník Ostrava in 2002. He played at the Bazaly until January 2005, making sixty-five appearances. Lička was a member of the squad of Baník Ostrava in the 2003–2004 season, when Baník won the league title. He was sold to 1. FC Slovácko where he made 28 league appearances in 2005-06 and was released in July 2006.
He had an unsuccessful trial at West Ham United and Leeds United before signing for Southampton F.C., following another trial. After an injury hit first couple of months at the club, Lička forced his way into manager George Burley's plans, scoring his first goal for the club in a 1–0 win over Stoke City on 21 October 2006. However not long after he became surplus to Burley's requirements and found himself playing in the reserves. After the appointment of new manager Nigel Pearson in February 2008, Licka was given a new chance and after a series of good performances found himself playing regularly again. However after the return of former Chairman Rupert Lowe, Pearson did not have his short-term contract renewed despite saving the club from relegation. Lowe did not offer Lička a new contract as he was also at the end of his contract. Despite reported interest from Pearson at his new managerial post at Leicester City, Lička chose to return to his homeland to play for Baník Ostrava. In June 2010 he signed for the French club Stade Brestois for three seasons. Lička curerently plays in Slavia Prague.