Actually, the "light year" is a unit of length that has its origins in Earth's movement around the Sun, but has since been detached from it.
The SI unit of length is the meter. It is defined as
the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second
The second, in turn, is defined as
the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom
By combining these two, we can define the meter as
the length of the path travelled by light in vacuum during the duration of (9 192 631 770 / 299 792 458) [which is approximately 30.663318988] periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom
This definition isn't very useful in everyday life, but it is very accurate and, more importantly in this case, has absolutely nothing whatsoever to do with Earth's size, or Earth's orbit around the Sun.
The International Astronomical Union goes on to define the astronomical unit as
a conventional unit of length equal to 149 597 870 700 m exactly
as well as, more importantly to your question, the day and century as
The astronomical unit of time is a time interval of one day (D) of 86400 seconds. An interval of 36525 days is one Julian century.
...which means that 100 years (one "century") is, by definition, equal to 36 525 * 86 400 seconds = 3 155 760 000 seconds. Remember that we already defined the second above.
One year is thus 1/100 of this value, corresponding by definition to 31 557 600 seconds, or approximately 2.90097e19 cesium-133 periods. Multiply this (a unit of time) with the speed of light (speed, which is distance over time), and what we end up with is the distance travelled by light in one of these years (a distance). Someone editing Wikipedia's page about the light year has looked up the exact value for us, and apparently by definition it is 9 460 730 472 580 800 meters exactly. This number is somewhat unwieldy, so we now choose to call this amount of distance "one light year".
Et voila, we have defined a year inspired by but eventually completely detached from the orbital period of the Earth around the Sun, and use this unit of duration plus the speed of light to define a unit of length. The unit of duration is arbitrary but defined, and the speed of light in vacuum is believed to be constant. The specific resultant value (the distance represented by this) has no immediate meaning; it just happens to be a somewhat useful unit for discussing moderate interstellar distances, and aligns with units that people in general are somewhat familiar with; there's no particular reason why the "year" couldn't be a purely scientific unit.
While it is certainly true that it's extremely unlikely that an alien civilization would come up with these exact contants (after all, there's nothing particularly universally special about 299 792 458 or cesium-133), with just a modicum of physics definitions knowledge, the definition of a light year could be translated into whatever some alien (or future humans; that would amount to about the same thing) culture uses, and we'd know that when we say "light year" and they say "przzqrtzfbn", we are talking about the same distance, even though we derive it differently. From there we can discuss amounts of distance in terms of multiples or fractions of this value.
The same, by the way, goes equally for all SI units, and everything derived from them.