A lawyer's overriding duty is to the Court. So if s/he has been told by their client that the client is guilty then they are in breach of the code of ethics if the lawyer represents to the court that the client is innocent.
There are a few misconceptions in this statement. Firslty, neither the client nor their lawyer can determine whether the client is guilty of an offence. 'Guilt' is a technical legal term which refers to the extent to which the Crown evidence is accepted by the jury, to the requisitie standard. A cleint can certainly give instructions to their lawyer which are consistent with allegations of fact asserted by the Crown, but it is not the job of the lawyer to conclude that this equates with 'guilt'. The duties of the defence lawyer when the client makes admissions to them are dealt with in previous posts. Moral guilt is a different phenomenon and has (for better or worse) little to do with the forsensic legal process.
A defence lawyer is not required to prove anything, and nor do they generally attempt to do so (except for some limited defences in which the onus of proof is reversed). They certainly don't make submissions that their client is 'innocent'. Nor is a court for that matter, convended to determine whether an accused person is 'innocent' of a charge. The criminal trial is designed to determine whether there is strong enough evidence to convince 12 people that the assertions made by the Crown are correct. If the jury finds that the evidence does not meet this standard, that's all they are deciding. A finding of 'not guilty' is a finding in relation to the quality of the evidence, not a finding of 'innocence'.
A defence lawyer, of course, represents to a court that their client is not guilty even where the client has made admissions that, if the jury heard them, may convince them otherwise. But this representation is one about the status of the Crown evidence, it is not a representation as to what their client did, or did not do, as a matter of fact. The lawyer may make allegations of fact in the course of the trial, when cross-examining witnesses for example, but these allegations will not be inconsistent with anything said to them by their client.
It is a very deeply seated misconception that crimninal trials in common law countries, such as Australia, are fundamentally a search for the truth. They are not. If what they produced was 'the truth' then guilty people would never be acquited and innocent people would never be convicted.