The term "light fighter" refers to a lightweight supersonic aircraft with after-burning engines and modern missile armament. The "light fighter" has almost half the capabilities of a "heavy fighter" in terms of combat range, combat load, cost of production and cost of operation.. In Cold War the "light fighter" had smaller RCS and could face any opponent in a dogfight. The idea was that since you go to war no matter what you are going to have losses; thus you need a large number of fighters available especially for the air-to-ground role...
In modern air warfare a "heavy" stealth fighter has lower RCS than any "light fighter". The BVR missiles are extremely reliable now and what it matters is the detection range and the number of missiles the fighter can carry.. Even the maneuverability of the fighter in close-range dogfights is not important anymore due to the new technologies (HMD, high off-boresight missiles, AESA radar, etc). What is more, "light fighters" have limited air-to-ground capabilities and can not be equipped with datalink- and network- electronic suites (no space, extra weight).
Therefore, the term "light fighter" is closer to "advanced trainer" and it is useful only to attack/support helicopters or intercept drones.
LCA should be a "middleweight" fighter like the Swedish JAS-39 Grippen with stealth characteristics and even greater payload.
It should be more expensive than LCA but still cheap enough for mass production..