Is Jean Valjean lying when he tells Javert that he will turn himself in after 3 days?

This has always bothered me. My impression here was that he was begging Javer for a chance, he made an offer which he would have stuck to (remember Valjean is not only a reformed man but believes his soul belongs to God).

However when Javer refuses his offer and pursues him he is no longer obliged to return.

A second theory is that when he met Cosette and took her away he realised that she needed him and prioritised her over his promise. Personally I think this is less likely as he's portrayed to be honourable and to keep his promises.

Actually, this is a point of discontinuity with the novel, wherein Valjean's promise to Fantine was simply to bring Cosette back to live with her and provide means for their support (not to care for her himself), as he expected Fantine to recover from her illness. Thus, he asks Javert for three days simply to get said affairs in order, which Javert denies him.

In the ensuing scuffle, Fantine dies in the hospital, and Valjean is captured by Javert and is returned to prison. After some time, he finally escapes and only then does he go to meet the Thenardiers, now with the new intention of remaining hidden from the law and caring for Cosette as a father, believing that rectifying his failure to Fantine is more important than continuing to pay for a decades-old indiscretion.

That he asks for 3 days time in the confrontation lyric in my opinion, represents a challenging part in the conversion process from book to musical. Going through the entire capture, conviction, and prison escape of the novel would be too long and cumbersome, but if Valjean simply plans from the start to flee from the law, it would make the honor and conviction of "Who Am I?" seem trivial or dishonest.

Thus, we are left with this slightly clumsy spot in the adaptation. I think the intention was to present what others here have suggested- that Javert's denial of Valjean somehow voided Valjean's responsibility to the law, and readers of the book will recognize Valjean's honest intent to do what is right in God's sight. However, the way his plan changes is never fully reconciled in the narrative of the musical, which can be confusing for those unfamiliar with Hugo's original.

It is likely that Valjean would have turned himself in. He struggles with this issue in the solo "Who am I?" and resolves that he is tired of lying and running and he should accept his punishment on earth as he will be rewarded in heaven.

However, Javert does not accept the offer hence Valjean is under no obligation to do carry out his end of it.

SPECULATION

Once he took on paternal responsibility for Cossete and began providing a loving homelife for her it would not have been in her interests for him to turn himself in.

I have been thinking about this quite a bit lately. My impression is that Jean Valjean lied to Javert twice in the movie about coming back and turning himself in. The last time when he begs Javert as they are sword fighting that he will return before he falls into the river. My impression is that if that was really Valjean's intentions then he would have turned himself in after completing his task because he is a man of honor and does not need Javert's affirmation in order to do the "right" thing. Those quote marks kind of indicate why it's a lie... because turning himself in is not the right thing to do.

Javert is an ass that would imprison a man for life for stealing a loaf of bread. That I think is the crux of the movie/play/book, Javert is an ass that doesn't understand any sort of reason and feels himself as the judge, jury, and executioner of anyone. His definition of "the law" really meant what he personally felt as good or bad, not the definition of "the law" that we commonly understand. One loan cop is not the moral arbiter of right and wrong much less deciding the fate of another mans entire life. So in the end I feel like Valjean lied to Javert (twice). Javert was a man that couldn't be reasoned with; he had no ability to see past what he personally wanted to a greater truth. So I feel like Valjean lied to Javert (twice) out of necessity.

What ultimately lead Javert to his death was his inability to reconcile how this seemingly unrepentant criminal (which he had judged as completely horrible, deserving of a horrible life in prison) can do such righteous moral acts like saving a prostitute and then further saving her child. Javert is an example of a person with completely rigid thinking; which is maybe an example of how people thought in past ages.

So.... all in all Valjean lied to the law, but he had to because Javert was a huge jackass with unreasonable expectations. JUST BECAUSE IT'S a LAW DOES NOT MEAN THAT IT IS RIGHT. Valjean decided on what was ultimately right and that is why I love this story :)