Learn Russian: Пусть они ищут новые средства. Нам не хватает финансирования. - Let them look for new funds. We lack funding.

This is the classic structure for expressing sufficiency or lack in Russian. The verb хватать (imperfective) or хватить (perfective) is used impersonally. The person who lacks something is the 'experiencer' in the Dative case (нам), and the thing that is lacking is in the Genitive case (финансирования).

Is хватает always used in the third-person singular like this?

Yes, when meaning 'to suffice' or 'to be enough/lacking', it is an impersonal verb. You will only see it in the 'it' form: хватает (present), хватало (past neuter), or хватит (future). There is no 'I lack' or 'they lack' conjugation; the literal translation is closer to 'to us it lacks of funding.'

How does Пусть work here to mean 'Let them'?

The particle пусть followed by a subject and a present or future tense verb acts as a third-person imperative. It is the standard way to say 'let him, her, or them do something' without using the verb 'to allow' (разрешать). Here, пусть они ищут simply means 'let them search' or 'have them search.'

What is the difference between средства and финансирование, since both relate to money here?