Having attended a Roman Catholic university for my doctorate, I must say that there is a massive incomprehension regarding the Lutheran doctrine of justification, as well as what's at stake in it in the minds of Roman Catholics.
In general, Roman Catholics assume that what's at issues whether or not grace is necessary for salvation. They define grace as a kind of divine power which makes us capable of living better. What they believe is that Lutherans are essentially ignorant and think that for Catholics there's no grace involved in justification or perhaps too little. They then go on to assume that if they can prove to you that they believe that no one can be saved without divine help, then all of your objections will some how go out the window.
If you read the text of JDDJ, this is basically the assumption throughout the whole document. When they're not pretending that the same words mean the same things in the different traditions (often times they will use "justification" "faith" or "grace" as if we agree what those things mean), the assumption is that Lutherans and Catholics agree that no one can be saved except by grace. Problem solved!
I would cite two major problems with this.
1. Grace is a meaningless concept if it does not involve a strict monergism. In other words, if I claim that grace is necessary to salvation, but then say that free will has a little something to contribute, it makes grace effectively meaningless within my system of theology. Why? Because without my contribution the whole thing would fall apart. For this reason, there is no functional difference between whether I did the whole thing on my own or I just did a little bit. At the end of the day, it all depends on me and hence I still have a reason to trust in myself. If I have a reason to trust in myself, then I am still curved in on myself and am not oriented towards the external grace of God.
2. The grace of God is a meaningless concept of it is not primarily an external judgment of God which I place my faith in. I say "primarily" because the Formula of Concord claims that the term "grace" sometimes means sanctifying grace in the NT. Interesting enough modern interpreters have not been so generous. According to Kittel's Wort-Buch of the NT, the word never means anything other than a forensic verdict.
In any case, the point is that grace radically reorients the self. By trusting in God's external judgment of grace, I look away from myself and to God. This restores the original relationship of receptivity that is natural to creator and creature.
This is why the Augustinian schema effectively doesn't work either. Even if I do posit monergism, but then say that it leads to my meritorious behavior and from there to salvation, then I'm stuck trusting in myself. Though I am intellectually claiming that God is doing all the work, I nevertheless existentially look to my own merits as a source of my relationship with God. In this I am still curved in on myself and dead in my sins.
Ultimately, what Roman Catholics don't understand is that the justification that the Reformation posited was justification by faith, not merely justification by grace (as Gerhard Forde has noted). The Catholic system is full of grace. And the end of the day though, it cannot allow for faith in the sense what we Lutherans have. The Catholic position cannot help but posit that we look to something other than the grace of God as an ultimate source of trust, whereas the Lutheran position looks to Christ alone.