Regeneration cycle

A life cycle refered to the set of regenerations, totaling twelve, which were possessed by a single Time Lord, allowing for thirteen incarnations before death. (TV: The Five Doctors) In certain cases, however, the Time Lords proved able to bestow additional regenerations. (TV: The Sound of Drums, The Time of the Doctor)

End of the cycle

Without access to additional regeneration energy, a Time Lord would ultimately perish at the end of their thirteenth incarnation. (TV: The Time of the Doctor)

In his thirteenth and final body, Azmael deliberately regenerated past his limit, killing him and Mestor, who had been attempting to possess Azmael's body after his own was destroyed. (TV: The Twin Dilemma)

As witnessed by the Sixth Doctor and Peri Brown, an elderly Time Lord at the end of his final life disintergrated as he "degenerated" into molecules. (COMIC: The World Shapers)

Beyond Thirteen

Despite the limit of thirteen lives, the High Council of Gallifrey possessed the ability to bestow additional regenerations upon individual Time Lords. While the Tremas Master was offered a complete life cycle by Borusa, (TV: The Five Doctors) the Eleventh Doctor was granted an indeterminate amount of additional regenerations through regeneration energy provided from Gallifrey. (TV: The Time of the Doctor, Kill the Moon, Hell Bent)

Without this option, certain Time Lords would seek to extend their lives through other means. Having used all his lives, the Master took to possessing the bodies of non-Gallifreyans. (TV: The Keeper of Traken, Doctor Who) In theory, Time Lords could also be robbed of their regenerations by others of their kind, as the Master attempted to do to the Eighth Doctor via the Eye of Harmony. (TV: Doctor Who)

In a story related by the Valeyard, the thirteenth final incarnation of the Doctor supposedly composed a set of scrolls which detailed his work to bypass the limit of twelve regenerations. The Valeyard's claim, however, was doubted by the Sixth Doctor. Indeed, the Doctor found what appeared to be his final incarnation on Etarho to be have been the Valeyard masquerading as him. (AUDIO: Trial of the Valeyard)

Individual cases

The Master

The Master had expended his initial life cycle, but cheated death by possessing the body of the Trakenite Tremas. (TV: The Keeper of Traken) In return for retrieving the Doctor from the Death Zone on Gallifrey, Lord President Borusa offered to bestow upon the Master a new life cycle. Ultimately, the Master did not receive the life cycle from the High Council. (TV: The Five Doctors)

Eventually, however, the Master, having been resurrected by the Time Lords to fight in the Last Great Time War, possessed the ability to regenerate again. (TV: Utopia, The Sound of Drums)

The Doctor

Another Time Lord who lived beyond their initial life cycle was the Doctor. (TV: The Time of the Doctor) Having abanonded their title for the vast majority of their ninth life, (TV: The Day of the Doctor) and distinctly retaining their current form following their eleventh regeneration, the so-called Eleventh Doctor was actually the twelfth incarnation and last of the first thirteen lives of the Doctor. On the verge of dying of old age at the Siege of Trenzalore, the Doctor was granted additional regeneration energy by the Time Lords through a crack in time above the planet, allowing him to resolve the conflict and regenerate for the thirteenth time. (TV: The Time of the Doctor)

However, the Twelfth Doctor remained uncertain of the amount of new regenerations he had access to, (TV: Kill the Moon) with even Rassilon not being sure how many were granted to him. (TV: Hell Bent) The Thirteenth Doctor was the second incarnation of the Doctor's second life cycle. (TV: Twice Upon a Time)

Proto-Time Lords

While possessing the ability to regenerate, the life cycles of the Proto-Time Lords created by the Kovarian Chapter were uncertain, with seperate individuals possessing different numbers of regenerations. (AUDIO: The Lady in the Lake) The original, River Song, regenerated twice before sacrificing the remainder of her regeneration energy to save the Eleventh Doctor from death. (TV: Let's Kill Hitler)