The phrase “lost in the department store” is a participial phrase since it acts as an adjective that modifies the noun “child”. The participial phrase in this case is formed by the past participle (lost) and objects or modifiers (in the department store).
An infinite phrase starts with an infinitive “to+ bare verb” and its complements or modifiers.
A gerund phrase always starts with a verb+ing form and functions as noun.
A verb phrase is the part of the sentence formed by the main verb plus modals or auxiliary verbs.
So the correct option is “participial phrase”