The Italians were the better side but wasted a hatful of chances and had to settle for a point.
The result has left Lazio second in the pool, two points adrift of group leaders Trabzonspor, who won 2-0 over bottom-side Legia Warsaw.
Limassol, meanwhile, stand third, one point adrift of the Romans.
The result in Cyprus will be of little comfort for Lazio coach Vladimir Petkovic, whose side went into the game looking to end a four-match winless run in all competitions.
The first chance came after 13 minutes as Fotis Papoulis' strike from the box went wide of Lazio goalkeeper Federico Marchetti's far post before Hernanes' bullet strike from outside the area went off target.
Lazio continued to press forward and before the break, Hernanes surged inside the area and fired a right-footed shot that went just wide of Apollon goalkeeper Bruno Vale's near post.
The visitors picked up where they left off after the restart and in the 53rd minute, Vale kept out Diego Novaretti's powerful header following a corner.
The home side gave themselves a good chance before the hour mark when Papoulis' left-footed strike from the edge of the area went just over the crossbar.
In the 62nd minute, Vale was forced to make a full-stretch save to clear Ederson's 15-yard attempt.
Apollon defended deeply as Lazio went forward in search of the winner and the Italian side should have gone in front with five minutes remaining.
Cristian Ledesma fed Hernanes in the box and he struck wide from a good position, before, seconds from time, Lazio substitute Ogenyi Onazi warmed the hands of Vale with a stinging drive from 30 yards which the keeper saved.