She grew up in Kyriat Bialik near Haifa and now lives in Haifa itself with her husband and three children. She was ordained at Israel's Rabbinical School of the Schechter Institute in 2004.
Her training in theology, psychology, and marketing were on display in her interview with me, in which some questions were stonewalled, some deflected - and some met head on.
We began with the issue with which she is probably most associated outside Israel: the bitter dispute over 'mixed prayers' at the Western Wall.
Recently three Israeli Orthodox Rabbis agreed that the Israeli government should allow the establishment of a section of the Kotel for men and women to pray together. What brought about this change?
"Because there are Orthodox Rabbis who are pluralists, there's a big change inside the Orthodox," she says.
"You can also see co-operation between the Conservatives and Reform which is not an easy thing. People are starting to understand that to proceed in Judaism is to work together and not to fight. The real fight is with the Charedim.
"In the beginning [of the protests] I was shocked because of the violence and it's really hard to hold a Sefer Torah and go through violence to get to the wall, but then it was very uplifting and I felt the Gates of Pearls opening.
"Twenty-five years ago they threw us out and we went quietly. Maybe we are provocative but it's not as if being quiet has done us any good.
"They don't accept my way of doing Judaism so I don't think we have any choice".
When challenged as to why Israel needs a Rabbinic human rights organization working on social and Palestinian issues, her faith is again to the fore.
"If you start at the beginning of the Torah, God is creating human beings and everyone is equal. The first thing we are taught is that everyone is equal, but even if I look inside the Green Line this is not the situation.
"In Israel, the voice of human rights in general used to be very quiet, and our organisation was established to give sound to this voice.
"We work with Palestinians, we work on education, social justice and inter-faith. Judaism has a message for everything - how we act as a community - and it's my duty as a Rabbi to say to the Jewish state if you want to be a Jewish state you need to remember the values that were here before you."
Asked if this is political, Rabbi Lev responds with one word: "No".
So, how does that square with being involved in politics?
"We do work around policy change. The left and right divide in Israel is along the lines of conflict, but if you look at the Knesset then some of the Likud would be on the left of the economic argument.
"In the Knesset we work with everybody. On the issue of human rights, then everyone who is prepared to work with me I will work with"
So why is she seen as a such a divisive figure, even accused of being an "enemy within"?
"The wide perception in Israel is that Palestinians deserve less than Israelis, and if you fight for Palestinian rights that means you help terrorists. For most people it's an equivalence."
Most people? She sighs: "More than half".
And why come to the UK?
"Because we think it's very important for our voice to be heard outside of Israel. People need to know there are other voices in Israel than the government."
One of the criticisms of Rabbis for Human Rights is that they are one-sided on the Palestinian issue. I ask if she believes any Jews should be allowed to live in the West Bank. "As an organisation we don't go into that. It's a political question and we don't get into political questions."
Does she want to answer it on a personal basis? "No".
And the security barrier? "I support the necessity for all of us to live in a secure world. The problem with the barrier is that they used it not only for security but as a political instrument to harm the Palestinians.
"If it was only for security it would be on the Green Line".
Lev is positive about a change she discerns since the so-called 'Tent Movement' of 2011:
"People in wider circles started to understand that a democratic country means not only voting once every four years but doing things between elections in order to have some sort of influence on the public discourse.
"I see it in the Knesset, where more people come to sound their voice. I see it in Haifa where people organize to sound a voice against racism, against discrimination against the Muslim and Christian Arabs in Haifa.
"It takes time. When the tent movement stopped a lot of people thought, 'ok, we failed'. But I said we will see the result after about three elections.
"The other change is that good people are getting into work at the government agencies. People see that work in government is something that they should do, that it's important. When I was twenty no-one thought about a career in government. That's changing and it's very good.
"On the other hand, there are forces trying to make us remember all the time why we should be scared of the Palestinians."
But what of the evidence that there are good reasons why people should be scared of some elements in Palestinian society?
"More people in Israel are killed by cars. One of the biggest problems is that we don't meet, Jews don't meet Palestinians, and when people start to know each other then they know that they are not all coming to kill each other".
