1. God did not lied. you are mistaken or missing the point.
2. Eve touched it and ate it.
* Spiritually speaking Eve died that day.
* Physically speaking Eve eventually died.
What God said was fullfilled. He did not lied. He never specified that they would die (physically speaking) at the very instant they ate or touched the fruit. He never specified that the death would occur 5 minutes or 5 hours after the event. He said they will die, and they did. There is no lie.
Does a judge who sentences a criminal to death is telling a lie because the criminal is not executed inmediately?
* No. The execution may occur months after the trial, and even the execution date may change / postponed due to appeals or other circumtances. But it is not a lie, the criminal is executed in due time.
How is that for a first lesson in the Bible, that God cheerfully lied to mankind?
* As said before, God did not lied.
And was Eve the world's first scientist?
* No Adam was the firt scientist, he started to catalog animals and giving them names. Eve came second.
... conducting a dangerous experiment to see if touching the Tree would kill her?
* that is not science, that is being foolish, irresponsible.
Is it any wonder she then went on to taste it, after she found out God must have been fibbing about the first part?
* You are implying that physical death was supposed to ocurr inmediately, and that is your error. By sinning she died that day, but physical death came later.