。
She looks lonely.
Literal
She [topic-は] lonely-looking appears.
寂しそうに見える combines two grammar patterns: ~そう (looks like, based on appearance) converts the adjective 寂しい into 寂しそう (lonely-looking), and ~に見える (appears/looks) adds the observer's perception. The そう is the appearance-based conjecture, different from hearsay そうだ. The adverbial に connects そう to 見える.