There is a Greek connection between some female goddesses with lions. Rhea for instance, as far I remember. These goddesses (or simple females) might be connected to Apollo (or somebody else).
Probably the city of Cyrene had a sort of symbol, as nowadays cities also have heraldic devices. In the case of Cyrene it seems to have been a lion. The Greek colonists, which founded Cyrene, probably came from a region, where the Apollo cult was strong. It's said, that it spread from Minor Asia.
The myth transports some informations about the real development, as usual.
Cyrene was founded by people of Thera (Santorin), which had populized the island Platea near to the coast of Lybia on the advice of the oracle in Delphi (sic - there is "Apollo") before. In the year 631 BC Cyrene was founded at the fountain Cyre (which was dedicated to Apollo - Apollo again), the Greek leader had the name Aristoteles and took the Lybian kingsname Battos. In the year 570 BC an army of Cyrene had a great victory against the Aegyptien king. 525 the Persian reignment was accepted. 322 the city was conquered by the Ptolomaians. Roman reignment since 74 BC.
Probably there were lions around Cyrene, which used the fountain.
More or less the "small Pauly" (that's a dictionary) thinks so. I think, that the small Pauly is mostly reliable.
Lion with Woman came from Kybele or Rhea - surely not from a small and late figure like Cyrene.
As Kybele was also from minor Asia, there might be a relation between Kybele-Apollo, but I think, the origin of Kybele is more southern minor Asia, and Apollo developed from the northern parts (probably, but this is discussed with many different opinions). At least Apollo fights with the Troians, not with the Greek.