Were there native Libyans who resisted Italian occupation and colonialization efforts? Yes. Did these resistance fighters want a democratic form of government? No.

The most organized and effective of the resistance movements against Italian occupation was the Senussi Order, founded by Muhammad ibn Ali as-Senussi as early as the 1830's in Mecca. They were followers of Sufism, best described as a form of Islamic Mysticism and were hostile to European encroachment in Sudan and later Libya.

After Italy's annexation of Libya in 1912, native Libyan clans along with the Senussis occupied various towns in Eastern Libya, the region known as Cyrenaica and declared their resistance to the Italian invaders. Actual Italian attempts to clamp down on the rebellions didn't take priority until the early 1920's, mainly because World War I was raging through most of the decade.

In 1923, the newly appointed Prime Minster, Benito Mussolini, declared a campaign to fully pacify Libya in order to open more regions of the country to Italian settlement, beginning a 9 year campaign against Senussi rebels, led by Grand Senussi Omar Mukhtar, that would last until 1932. The 'Pacification' was characterized by mass killings of the native Cyrenaican populations, openings of concentration camps to detain ethnic Cyrenaicans and other suspected rebels. Without concrete numbers, the most solid source I have places the number at ~225,000 Cyrenaicans killed as a result of the campaigns to crush rebellions in Libya.

Senussi and all other rebel activity was effectively crushed by 1932, with Omar Mukhtar captured outside of the town of Slonta in September of 1931 and hanged, leaving the rebels essentially leaderless, with Field Marshal Pietro Badoglio proclaiming an end to the campaign that January of 1932.

But with the rebellion defeated, the Senussi Order wasn't fully destroyed, with local rebels supporting British forces as the Italians retreated across Libya during World War II. On December 24, 1951, Muhammad Idris bin Muhammad al-Mahdi as-Senussi, the Chief of the Senussi Order, became the first King of Libya upon its declaration of Independence until 1969, when he was overthrown by General Ghaddafi.

Sources:

Gooch, John. Re-conquest and Suppression: Fascist Italy's Pacification of Libya and Ethiopia, 1922–39. Journal of Strategic Studies. 2005.

Edit: typos