Lark's mother was a pegasus in Commander Hurricane's army, and her father was an earth pony hermit.
Lark doesn't know much about her parents' relationship--she hardly ever saw the two together. She spent the majority of her childhood with her mother at the fort.
When Equestria was founded, Lark and her mother set out, but her mother--by then rather old--did not survive the journey. Lark's father did, though, being of sturdy stock.
Her father retired to another cave, and hasn't left.
Lark doesn't keep her father's reclusive nature a major secret, though she dislikes talking about it. The real secret is that her father is far from self-sufficient.
Indeed, he isn't sufficient at all. All he does in his cave is meditate. Therefore, Lark must make the trip every month over the mountain and into the cave, bringing him food and other amenities.
Of course, this isn't easy for Lark. The cave is far from civilization, and she must therefore fight her way there. As her arbalest broke on the last outing, the next trip will be especially dangerous.
Besides which, Lark has trouble affording the supplies. A long time ago, her mother badly injured a unicorn she'd had a long-standing rivalry with.
The daughter of that unicorn is now a secretary of the state, and the rivalry has passed down to the next generation. The secretary has ensured Lark is as close to penniless as possible.
Lark isn't sure where the money for the supplies will come from next. Only one thing's for sure: she is not looking forward to the next departure.