This is often repeated but is historically VERY incorrect. Yes, Israel does lobbying in the states and does influence (like every other country). The current Israeli government is indeed terrible and blatant at that.
However, Israel left Gaza in 2005 with no deal as part of US pressure (which led to the current situation). Israel offered a Palestinians a country which included east Jerusalem twice based on US pressure. Israel left Lebanon alone due to such pressure.
Israel didn't attack Lebanon for a year and tried to settle due to US pressure despite an average of 25 rockets per day towards civilian population.
Imagine a country being attacked and fired on for nearly 20 years (by Hamas) and keeping reposes "moderate". That's US pressure and influence right there. Israel delayed going into Rafah due to US pressure, it turns out Sinwar and quite a few hostages were there...
The reason it seems that US pressure isn't working is mostly because no one knows what to do exactly. Hostages are still held by Hamas. Hezbollah is still firing rockets/drones even now. I'm 100% for a hostage exchange but right now there's no deal, part of that is because of Netanyahu (who is terrible) but not all of it. The US can't fire Netanyahu (I wish they could...), and that's a problem. They want to strengthen anti-Netanyahu forces within Israel while still moderating its actions, that's a very tight rope to walk on.