Exhaust for dueling potential or vs divers.
Ignite is better used on Bruisers, Mages and supports. It will give you a bit of added kill pressure early on but the trade off of survivability isn't worthwhile. You're likely to deal more damage by surviving longer.
Note:Ignite deals (at most) 82 damage per second. Most champions, Marksmen especially, are capable of dealing more DPS with a single damage item.
Example: At level 18 Ignite deals it's maximum of 82 damage per second (DPS). Lucian's base DPS with standard runes and nothing more than a Doran's blade will deal ~79 DPS with auto attacks alone and about 142 DPS including abilities.
At level 1 Ignite