There are three things the Licho does really well.
TL;DR: Use Licho vs packs of MOBILE targets, IMPULSE and AoE!!!
The first, is it's an IMPLOSION bomber, that means massive negative impulse. This adds 1000-2000 damage to a target like a reaper, and 2000-3000 (thats a 1-shot) to a target like a Jack. IN AN AOE!! This OBLITERATES things like tight groups of ravagers (where it can kill 4-10), where 4 shadows can kill 2, MAX.
Even vs static targets, the Licho's primary advantage is that it can survive 2 hacksaws. Sure, it has half the hp/cost or damage/cost of the Shadow, but whereas attacking under a hacksaw + light AA will mean you lose 1-2 shadows, attacking that with a Licho means you'll lose nothing. This isn't academic, I've had this done to me and done it to others, where you build enough AA to start whittling down his Shadows and think that, even if he does attack you'll make cost, and instead he swings in with Licho's.
While being about half the power/cost of the shadow, it also does this damage in about 3/4ths of the AoE of the firestorm. This makes it way more versatile, being able to be used against land armies up to reapers (Try using firestorm on a pack of reapers...) and single heavy units just as easily.