In the first example, the verb “became” is also referring to the lake. In this case, when using a coordinating conjunction, if one does not put a comma, it is perfectly fine to skip the verb, meaning the first verb applies for the second part of the sentence.
A simpler, more familiar example would be:
“The boy ate the apple and the banana. “
It is needless to say
“The boy ate the apple and the boy ate the banana.”
Similarly, if the subject is to change, we can still omit the verb and mention the new subject:
“The boy ate the apple and the girl the banana” in the same style as the Harry Potter quote.
The 2nd paragraph is a different situation. The sentence “his lamp bobbing away into the darkness” is a modifier for Filch. In this situation, it is the equivalent of saying “with his lamp bobbing away into the darkness”. The modifier is not a complete sentence, it is an incomplete prepositional phrase. Here the linking conjunction/preposition is omitted, but the modifier is still a phrase, meaning it is not a complete sentence with a subject and a verb. “Bobbing” is a participle adjective describes the lamp, and is not a verb for the “lamp”.
In conclusion, since both examples are incomplete phrases that rely on what comes before them, they do not need to have a subject and a verb. The first example has an implicit verb from the part before it, while the second example doesn’t have a verb since it is a modifier phrase, and is incomplete.
Best Answer
This construction is fine; was is a copula (or linking verb); the infinitive phrase watch from outside is the subject complement.
The infinitive marker to, which I inserted, is optional. According to The Cambridge Grammar of the English Language,
Edit to Answer Further Queries
The verb was in
is not an auxiliary verb; it is a linking verb.
As for auxiliary verbs (or helper verbs),
Hence for was to be an auxiliary verb, watch would need to be a main verb:
That's not the case in OP's example, where watch is an infinitive.
Collins Dictionary explains further, that the verb be is also used as a main verb. It is commonly found joining a subject to its complement..