Well, he certainly proved himself to be capable to crush the Ottomans, but keep in mind that Timur Lenk's great flaw,
was that - although he was a great conqueror - he was also a relatively poor empire-builder.
I may have to brush up my knowledge of the history of Timur Lenk's campaigns, but IIRC his empire constantly suffered from rebellions and local uprisings as soon as his armies were gone, and this may have been because of a poor, rather inefficient administration.
...and if I am correct in this, then it is quite unlikely that Timur Lenk's empire would ever be as much of a threat to Europe as the Ottomans were, because Timur's empire would simply fall apart after his death, and the Christian nations of Europe, as well as the rival Muslim nations (both the subjected as well as the independant nations - Timur Lenk wasn't exactly loved by the other Muslims either...) of west Asia would deal with Timur's successors relatively easily.