Timur the Lame, who is better known in the West as Tamerlane, is related to the Ottoman Empire because he was a major foe of that empire.
In the late 1300s and early 1400s, Tamerlane and his armies attacked the Ottoman Empire. Tamerlane himself was a Muslim of Mongol heritage, but he felt that the Ottomans were not legitimate rulers. He therefore saw himself and his warriors as "ghazis" or holy warriors even though they were fighting fellow Muslims.
Tamerlane was able to defeat the Ottomans in many battles. He took cities such as Damascus and Baghdad, both of which were part of the Ottoman Empire. He also managed to capture the Ottoman Emperor of the time, Bajazed. This led to a period of chaos in the Empire.
Timur's relation to the Ottoman Empire, then, is that of a foe and a conqueror.