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If a gerundive is used with non, can it mean both lack of obligation and negative obligation? For example, can non loquendum est mean both "it is not necessary to speak" and "it is necessary not to speak"? Does the word order have a role here?

If you want to argue that a gerundive with non can have a certain meaning, can you please provide a classical quotation where the meaning is clearly only one of the two possibilities? In the cases I have seen, I find it hard to decide whether a lack of obligation or a negative obligation was meant.

To me the literal reading of such a phrase is lack of obligation, but negative obligation is possible too. This was discussed in connection to the earlier question concerning negative obligations, but I wanted to ask this separate focused question to settle this matter.

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The following examples are of the negated gerundive clearly equivalent to a prohibition.

The pair faciendum / non faciendum is used to indicate positive and negative obligation, as evidenced by the parallelism with sequi / fugere.

Videsne ut quibus summa est in voluptate perspicuum sit quid iis faciendum sit aut non faciendum? ut nemo dubitet eorum omnia officia quo spectare, quid sequi, quid fugere debeant? (Cic. De Fin. 4.17.46)

The grammarians consistently use dicendum and non dicendum to mean "an obligatory expression" and "a prohibited expression."

Mi Paula et mi Aemilia non dicendum, quia mi masculini est generis
pronomen, non feminini, et ortum est a prima positione meus; sed dicen-
dum
mea Paula et mea Aemilia, o meum caput, o meumque brachium. (Flavius Caper, De Orthographia, 102)

Legal Latin frequently uses the negated gerundive to signify prohibition. (The Digests itself is post-classical but consists largely of extracts of earlier Latin.)

Proculus ait ... [in a case where one crime/tort could be prosecuted under two different legal statutes] si uno iudicio res esset iudicata, altero amplius non agendum. (Digesta, 9.2.27.11.3)

A slightly post-classical example clearly signifying prohibition:

quod in facto reicitur, etiam in dicto non est recipiendum. (Tertullian, De Spectaculis, 17)

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How about "non loquendum est" = literally: "it ought not to be spoken"; equivalent to "it must not be spoken"; therefore your second choice: "it is necessary not to speak".

Suspect that if you want to introduce "necessary" you may have to deploy "necessitas"; not the gerundive-of-obligation impersonal-construction.

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