Let us examine your statement:  "Maybe we learn that we should not love a person so much so that the relationship can last longer?"  This statement underscores precisely the theme of one of Friar Laurence's didactic speeches.  In Act II, Friar Laurence instructs Romeo,

These violent delights have violent ends,

And in their triumph die, like fire and powder

Which as they kiss consume.  The sweetest honey

Is loathsome in his own deliciousness

And in the taste confounds the appetite.

Therefore, love moderately, long love doth so,

Too swift arrives, as tardy as too slow. (9-15)

Clearly, your statement touches upon the response in the previous post; that is--to use academic language--the theme of impetuosity.  For, this theme is prevalent throughout the play as almost every character exhibits irrational haste, even the Friar himself as, in fear, he runs from Juliet's tomb leaving her alone.  So, stay with your original idea and develop it, since often our initial reactions to a literary work are intuitively accurate.

As you look for support, consider the hasty actions of Lords Montague and Capulet as in cholera, they wish to duel in the streets of Verona even though they know that such actions are against the law.  Likewise, Mercutio and Tybalt engage in heated words and impetuous actions, along with Romeo, who hastily intervenes--albeit meaning well--and causes Mercutio to be gravely injured. 

Most impetuous of all, Romeo wishes to marry Juliet immediately because their erotic love is a "violent delight" that they wish to satisfy.  The tragic end to their love is due to this haste.  Indeed, how often the satisfaction of one's erotic feelings prevents the development of a lasting relationship in real life. Studies have shown that if couples will really get to know each other over time, they will develop a more meaningful and lasting relationship, one which can withstand conflicts and difficulties.  (For support, you may wish to do some research on this last idea as magazines have featured such articles.) At any rate, time and time again throughout the play, poor choices because of haste are more the cause of the tragedy than the cursed fate.

I do not really think that the moral of this story is about parents and obeying.  I think that the moral of the story is not to be so stinking impetuous and uncontrolled.

In this story, Romeo and Juliet die because they cannot control themselves to any significant degree.  They cannot step back from their passion and put any thought at all into what they should do next.

So to me, whether they should have obeyed or whatever is sort of beside the point.  To me, the issue is that they were not mature enough to think about what to do so they got themselves in trouble.

In the play 'Romeo and Juliet' by William Shakespeare, the author shows us that there is much to learn from the tragic end of the tw young sweethearts - and that is not only applicable to young people. Yes, Romeo and Juliet did lie to their parents when they got too carried away - but the question also is about why they felt they needed to lie. They needed to lie mostly because neither felt safe confiding to the adults in their extended family - they had probable learnt from past experience that they would not be listened to let alone have their wishes considered. For example, see Juliet's situation in the scenes where she tries to explain her distress first to her mother, then to her father. They have learnt that their needs will always come last before the needs of the two families - to feud pointlessly.We have learned how damaging it can be not considering childrens needs.

The answer obviously depends on who you ask.  You could certainly assert that there are moral lessons about lying to your parents, but you could also argue that it makes a moral statement about the lack of involvement or the decisions that parents force onto their children.  Who knows how things might have been different if both Romeo and Juliet had spoken at length with their parents about their feelings.  Of course this isn't the action of the play, so we'll never know, but a similar question could be asked of the parents:  Why didn't you sit down with your children and ask them carefully and lovingly what was causing this tempestuous behavior?

You might also look more carefully at the demands for revenge, as the previous poster said.  When you are enraged by the death of someone, stop for a second and think about how causing the death of someone else is going to solve the problem?