This is determined on a case by case basis in a context rich way. There is almost no such thing in the law as a rule that applies in all circumstances without exceptions.
Anything knowledge of a lawyer is generally attributed to the client as a matter of law, whether or not the client has actual knowledge of the fact. How lawyers and clients choose to communication is up to them, and what ultimately matters is what happens that causes the client to take some particular action in reliance on the belief that there is an agreement and not merely when someone knows something which is somewhat esoteric.
If the preconditions were not met, but believed to have been met, there are a couple of remedies available to the client who relies on their own lawyer's statement. One is to sue to rescind actions taken in wrongful reliance on the existence of a contract and seek restitution. The other is to sue one's own lawyer for getting it wrong if damages are suffered as a result, although there might be a duty to mitigate by taking the first course of action first.
A statement from an opposing counsel is equivalent to a statement from an opposing party and would have the same legal effect as a misrepresentation by the opposing party (presumably in this context, a negligent misrepresentation, rather than an intentional one).
But this is all very context specific. It depends upon what action is taken in wrongful belief that all preconditions were met, the nature of the preconditions, and whether there are some other related obligations that could compel someone to carry out a precondition in the face of performance by a counter-party when the precondition was not actually met.
For example, if the precondition involved signatures by officers of affiliated companies and one affiliated company didn't sign, that company could very likely be compelled to sign if the other party acted in good faith reliance on that condition being met and this wasn't promptly brought to the reliant party's attention.
Similarly, if the written agreement memorialized finally, an oral agreement which was not subject to the statute of frauds, or which was brought out of the statute of frauds by part performance, there may already be a binding contract before all of the formalities are complete.