'No further action' doesn't mean that the Crown Prosecution Service has decided that the accused person (i.e. your son) is innocent. It simply means that they've decided that there's insufficient evidence to convict him. (i.e. they might still consider that it's possible, or indeed likely, that he committed the assault but they simply can't prove it in a court of law 'beyond reasonable doubt').
Therefore it doesn't automatically follow that, because they've decided on 'no further action', that they believe that his ex was lying. Even if they do so, they might well have decided that they can't prove it 'beyond reasonable doubt'.
Ask yourself what you would do if you were on a jury and a defendant was accused of wasting police time (by falsely accusing someone of assault) but that defendant simply said "I didn't waste their time; it really happened". Unless the Crown Prosecution Service could clearly show that the accusation MUST be false (e.g. because the person accused of carrying out the assault was abroad at the time that it allegedly happened) how could you be TOTALLY sure (beyond all reasonable doubt) that the defendant hadn't actually been telling the truth? Unless you were COMPLETELY convinced that they'd DEFINITELY lied to the police, you would have no alternative but to declare them 'Not guilty'. So the CPS know that without CONCLUSIVE EVIDENCE that a person MUST have lied to the police, there's absolutely no point in charging them with 'wasting police time' (as they're bound to be acquitted).
If you're aware of evidence which could PROVE (beyond all reasonable doubt) that your son's ex lied to the police (such as texts sent to him, by her, making it clear that's exactly what she planned to do) then you should contact either the police or the CPS to lay that evidence before them. Otherwise it's simply one person's word against another and no court of law would be able to convict her if she pleaded 'not guilty'.