Certainly, a judge's determination as to the honesty, and therefore integrity, of a party to a divorce as to financial matters can affect a decision to be made on other issues such as child custody, etc., but it is not an automatic guarantee that it will result in your ex being denied custody, if that is what you are thinking. Discuss this with your attorney, as to the best way to use this supposed falsehood to your best advantage.
Speak to your attorney about this issue and they will be able to put it in front of the judge in an appropriate way. If a party lies to the court and they are caught, it does not help them as far as their credibility and they could face sanctions and possible criminal consequenses for perjury. While the judge might consider the liar's character in determining custody and give you primary or more visitation, it is unlikely a judge would prevent the children from seeing their mother under the circumstances.
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As the other attorneys have stated, if she is caught in a lie it will affect her credibility which will likely cause the judge to place less trust in some of her answers as the case goes on. I don't think lying about a financial matter would or should affect a custody decision however. Most judges (and most other people) believe that a child deserves full and equal access to both parents. A lie doesn't make her an unfit parent per se and in and of itself it will proably have little to no effect on custody.
One important thing to remember is that judges are human. If a person lies to the court, it will cause the judge to question the credibility of all the testimony given by that person at trial.