I think you meant "Does Bomberman have a lore?"
With a post titled "Bomberman has a lore?", I was expecting the post to be either surprised that Bomberman has a lore, or surprised that someone would have said Bomberman has a lore.
Especially when paired with the picture of a game's boxart, I thought that this post was about something lore-related on the box or in its artwork.
As to where to find the lore, I'd check the manuals, including manuals from other regions. For a lot of the 90s, the manuals were the best (and occasionally only) place to find lore!