A pronoun that modifies a gerund or a gerund phrase should be in the possessive case (my, our, your, his, her, its, their). A gerund is a verb form ending in -ing that functions as a noun. Gerunds frequently appear in phrases; when they do, the whole gerund phrase functions as a noun. (See 48b.)

Your modifies the gerund phrase being hit by lightning.

Nouns as well as pronouns may modify gerunds. To form the possessive case of a noun, use an apostrophe and an -s (victim’s) or just an apostrophe (victims’). (See 36a.)

The possessive noun aristocracy’s modifies the gerund phrase exploiting the lower classes.

Gerund phrases should not be confused with participial phrases, which function as adjectives, not as nouns: We saw him driving a yellow convertible. Here driving a yellow convertible is a participial phrase modifying the pronoun him. (See 48b.)

The choice between the objective case and the possessive case depends on the meaning you intend; sometimes the distinction is subtle.

In the first sentence, the emphasis is on the people; we watched them, and they happened to be dancing. In the second sentence, the emphasis is on the dancing; we watched the dancing—a noun form modified by the possessive their.

note: Do not use the possessive if it creates an awkward effect. Try to reword the sentence instead.