Not much is known about Dirk, except that he forged the Eternal Ring a ring that allows even a human to wiled the Eternal Sword. Early in the game he mentions that he has a present for Lloyd when he comes back all grown up. It turns out this present was none other than the "Vorpal Sword" which, apparently, Dirk forged himself. Dirk is quite famous in Sylvarant getting forging requests from people all over the declining world.
In my opinion, some people may say that since Lloyd has two fathers, Kratos Aurion and Dirk Irving, that they are gay. However, Dirk and Kratos are not married, plus Kratos was already once married to Anna ??? (maiden name unknown). Otherwise Lloyd would not have been born, thereby relinquishing that suggestion forever.
Dirk found Lloyd in the Iselia Forest. However, if you chose Kratos to in the nighttime Flanoir scene, you will discover that Dirk actually received Lloyd from Anna right before she died in human form. She managed to regain control temporaraily
long enough to beg Dirk to look after Lloyd as Kratos was wounded at the time. However, after his recovery, Lloyd still remained in Dirk's care.
Reason number 1.
Kratos had lost the will to fight back and rejoined Cruxis after betraying them, after learning of Mithos' true intentions.
Reason number 2 being...
Kratos had left Iselia Forest and Iselia for that matter.