That will all get sorted out in discovery, settlement and perhaps a trial. Unless the other attorney ABSOLUTELY knows his client is lying (and this is hard, because an attorney is bound to believe his own client unless his assertions are ridiculous on their face), he can make the claims on behalf of the client.
I'd be willing to bet that that your attorney cares not one whit about "upsetting" the other lawyer, but often at the initial pleading stages, all kinds of spaghetti is thrown at the wall to see what sticks as the proceeding moves forward. It's just not worth getting upset about, because pleadings aren't taken all that seriously and it's felt that "it will all come out in the wash".
And usually, it's not that "the other attorney lied", but that his CLIENT that told him the facts "lied" (at least to your way of thinking about what the truth is). At this stage of the game, it's like "liar's poker" and there's a lot of posturing and "bluffing". Ask Avvo and your attorney again after there are depositions if the other side is still maintaining its counterclaim.
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Frequently, counterpetitions and counterclaims contain language which reverse the original accusation, making the accuser the accused. Divorce cases are a prime example. Without knowing what sort of case you have, it is not really possible to respond. Furthermore, opposing counsel has not lied. Assuming the counterclaim was prepared by opposing counsel on behalf of his client, these are not really the words of the attorney. Whatever the issue here, you have a lawyer and should be discussing it with him/her. In the long run, this matter should get straightened out during the pendency of the proceedings and if the alleged false allegations are serious enough, you may have a basis to seek damages under Supreme Court Rule 137.