Russia continues to press its advantage while it can:
Russia could choose to back Hifter and authorities in eastern Libya and help tip the balance of power in favor of the LNA to capture Tripoli and control most of Libya's territory and energy sources. The Admiral Kuznetsov’s visit to the Libyan coast and hosting of Hifter onboard — which did not go unnoticed by Libyans or international media outlets — is a hint that Moscow is edging toward this option. This would mean greater involvement by Russia and require a significant amount of resources, which Moscow might not have given its heavy involvement in Syria and its suffering economy.
If Russia has such ambitions, recall that Libya once hosted Soviet military assets. Having bases there again would bolster Russian efforts to control the eastern Mediterranean--already improved with the seizure of Crimea which serves as a power projection platform, bases in Syria, port access in Cyprus, and improved relations with Turkey which controls the Turkish straits between the Black Sea and the Aegean Sea entry to the Mediterranean Sea.
Recall too that Putin would see this outcome as revenge against America which took a 2011 no-fly UN resolution about Libya (that Russia did not veto) and twisted it into regime change. Russia resents that bit of sleight of hand.
Sadly, we led from behind so far back that all we did was destroy the old regime rather than change the regime into something better. The continued factional division and warfare in Libya has left room for Putin to enter yet another conflict zone to gain advantage.
This is all the more reason not to ease Russia's financial burdens in short-sighted deals over Ukraine or Syria.
UPDATE: Italy? Will you be happy with a Libya in chaos under Russia's gentle embrace? Or would Russian bases there be even better?