Lucas was two when the Galbadian Army invaded Dollet. His father was in the Dollet Army and survived the Siege of Dollet only thanks to SeeD; shortly after the Dollet Army was absorbed by the Galbadian Army as part of their settlement he transferred to the Reserves in disgust (a technicality: he didn't end up serving again), refusing to guard Dollet's radio tower on behalf of the Galbadian Army. As his father felt he owed his life to SeeD but was too old to join himself, Lucas grew up being poked to go to Garden and watched his older brother graduate SeeD. (Lucas is the youngest of three, with an older brother and an older sister.)
However, Lucas wasn't so keen on joining up, and was fairly content to live out his days in Dollet. There were cute girls to flirt with and tourists to hear stories of the outside world from. What more could he want? Sure, SeeD get to see the world, but learning to kill at a young age just seemed messed up, and he hardly wanted to risk his own life.
As soon as he was legally able to, Lucas dropped out of high school to kick around at different jobs around town; his previous jobs have included construction work, bartending, being a mechanic at the car rental, and an apprenticeship at the hairdresser's. His mother worried that her youngest would never hold a steady anything (job, girlfriend (hey, she wants grandchildren), house) and got him a job as a kitchen hand in the same hotel she worked at in the hopes that he'd settle down a bit if she could keep more of an eye on him. (Lucas's mother is the Dollet Hotel clerk whose accent bothered the new girl just hired in Final Fantasy VIII.) There one of the line cooks saw himself in Lucas, and began training him as an apprentice.
Lucas would still be there now if his father hadn't recently fallen ill. With his SeeD brother not sending much money home, his sister away at university, and his mother taking on less hours at work in her old age, the medical bills haven't been a welcome addition to the family. As there didn't seem to be many higher paying jobs that he was qualified for in Dollet, Lucas decided to take the plunge and head to Garden, where he hears the pay is better, and with his food and housing provided, he could send most of his paycheck back to his parents. Besides, maybe if his old man does kick the bucket, he'll at least finally have helped SeeD out in some capacity.