It is partially true that the Israeli lobby does exist. Just like every other lobby in the US government. Every major corporation has a say. It's not just the Israelis. Trump doesn't want a nuclear war in the middle east which would destroy the global economy and result in massive hyperinflation in addition to the loss of tens of millions of lives. Iran hates the West. Iran hates Israel. The reasons are very complex. But basically it is a fundamentalist islamic government that rules Iran. And if you're a religious fundamentalist, Western values are kind of disgusting and degenerate. And I from a non-religious standpoint actually agree to an extent with the critiques of Western culture. The Iranian government is fundamentally opposed to the West and they see the West as colonists and imperialists. And they see Israel as a colony of the West, of the United States. And because of that they are opposed to Israel and they are sick of being exploited and controlled by foreign powers. Can you really blame them? So because of all this, they're tired of the influence. And the best way to have leverage is to have nuclear weapons. If you have a nuke, you got a lot more say in global affairs, than if you don't. Because you can inflict massive devastation on your enemies. Now let's look at from the Western perspective. Israel has a bunch of nukes. Iran is trying to get nukes. If Iran gets a nuke, they could potentially target Israel. That would probably be their first target. And then after Israel they could potentially have other targets (e.g., Europe, US). And nobody wants big boom-boom bombs to go off in Israel or the US. If you're a rational person and you're from the West and you want to lookout for the interests of the West, you don't want any nukes going off in Israel. Which basically is the US's colony and aircraft carrier in the Middle East. Iran has many times said that they fundamentally hate the West. The US government is not going to let their colony of Israel be threatened or let Iran potentially use that nuclear weapon. Israel is a very important player in the Middle East and to America. Israel is supremely important to the American both on strategic grounds and on religious grounds. Most Christians are actually pro-Jew. Jesus was a jew. Christianity and Judaism are very closely linked. And because of that and because Christianity is kind of descendent in a way from Judaism, a lot of Americans are pro-Jew and pro-Israel. Especially the religious Americans. So for both strategic and religious reasons, America is always going to back Israel. America is not owned by Israel. America owns Israel. The US gives them money, the US supports them for American interests. Thats the truth. If we didn't have any religious ties and the US didn't really need Israel, America wouldn't support them at all.
Don't want a nuclear war in the middle east, don't want a nuclear bomb going off in America, or Europe, whatever. That is a possibility if Iran can develop nuclear weapons. As a nation you have to protect your peoples interests. Does America always do that? No. But America gives the Israelis money, the Israelis fight the Americans wars for them, and then when the US needs to they fly some bombers, nobody (Americans) die, they drops some bombs, and fly away.
TL;DR Israel is a very important strategic parter for America and there are a lot of religious ties and that's not gonna change.