The league is a ancient unit of length that doesn't below to a unit system. Its symbol is simply - league.
It was originally an ancient Celtic unit as well as being common in Latin America and meant the distance "a person could walk in an hour". It is no longer a recognised unit in any nation.
Once it started to be quantified, in Argentina (legua) it represented 5.572 km, in England it was quantified as 3 miles and at sea a league is 3 nautical miles (3.452 miles).
The light year is a unit of length in the Astronomical system of units. It uses the symbol ly.
Often confused with a unit of time as it contains the word "year", it is actually defined by the International Astronomical Union (IAU) as the amount of distance that light travels in a vacuum in one Julian year (365.25 days).
Using the speed of light (299,792,458 m/s or 'c') and the Julian year (as apposed to the Gregorian year which is 365.2425 days), we can equivalate 1 light year as 9,460,730,472,580,800 metres or ≈ 9.46 trillion kilometres.