"I'd a lost my job" means "I had lost my job". The contraction is for "I had" not "I would".
The "a" in front of the "lost" participle is interesting.
This is not simply a regional dialect, but is deeply rooted in English morphology.
It is a sort of prepositional prefix which indicates being in or on something, or in the middle of an activity (if applied to a verb).
For instance to "come a knocking on someone's door" or to "go a walking in the park".
There are English words which incorporate this "a". If you are sleeping, you are "asleep". Or if you see something ghastly, you can become aghast. Words like "aboard", "ahead" and "alight" follow a similar pattern.
What is dialectal, perhaps, is overuse of this "a" prefix: applying it liberally and perhaps inappropriately to all kinds of verbs in nearly every spoken sentence.