More Than Just a Yes or No Question
Can Israel develop its own stealth fighter jet?
There is a big difference between "could" and "should", as I will explain momentarily.
First, there are a few misconceptions that I need to clear up.
Also, the U.S. is not sharing stealth technology. So where is ISRAEL going to get it. Developing it is very expensive.
There have been rumors flying around for some time now that the Israelis either already have, or are at the very least developing a new line of low observable UAV's. In recent interviews, Israeli developers have even acknowledged that they are working in this direction:
Experts Look At Next-Generation Israeli UAS | AVIATION WEEK
To quote from the father of Lockheed Martin's stealth program, the four secrets of stealth are "shape, shape, shape, materials". With modern computational capabilities (which can make ray tracing routine), designing the shape of a stealth vehicle is not as difficult or expensive as it once was. In terms of radar absorbing coatings, the Israelis have already acknowledged progress in this area.
Israel's secret new weapon? - Israel News, Ynetnews
For an industrially developed nation like Israel (or Europe, or Japan for that matter), the real cost for developing a stealth fighter today would not be in developing the stealth technology. It would the cost of developing and fielding a new fighter.
The next problem was that they were designing an aircraft with little if any advantage over the target, the F-16. The LAVI would not have been able to match the outstanding range of the F-16 and probably could not exceed the F-16's performance limits in a dogfight. SO WHY BOTHER WHEN IT WOULD COST TWICE AS MUCH OR MORE?
Although I agree with many of the points that JIM made in his post above, he was dead wrong on this one. The F-16 was developed as a lightweight, air-to-air fighter first, with a secondary air-to-ground mission. The Lavi was developed as an air-to-ground fighter with a secondary air-to-air mission. In terms of range and payload, the Lavi far outstripped the F-16s available in its day, offering the range and payload of a Block 52+ F-16I in an airframe with the empty weight of a Block 10 F-16A.
The Lavi was ultimately cancelled not because the Israelis didn't want it, nor even because it was inherently more costly than the F-16 or other alternatives - but because it was more costly at the production volumes that the Israelis could afford. When the Lavi program was launched, it was built under the assumption that the Israeli air force could afford to buy 300 such airplanes. By the time that they were ready to sign the production contracts in 1987, however, it had become apparent that the Israelis could afford - at best - half that number. On a production run of 150 airplanes, the Lavi was no longer cost effective.
So back to the original question. Could the Israelis develop their own, indigenous stealth fighter? Yes, they most certainly could. There are even some in Israel who have suggested that Israel should take this route:
http://www.haaretz.com/print-edition/opinion/f-35-take-it-or-leave-it-1.304297
The Israelis are not entirely satisfied with the F-35. The US has agreed to allow the Israelis to include Israeli communications gear in the F-35, but they have refused to allow the IDF to integrate Israeli electronic warfare systems. This has been a big sticking point for some time.
Israeli analysts at odds over purchase of F-35
The F-35 also does not have the range that the Israelis would have wanted. The F-35 was sized around the requirements of the most technologically difficult of its three variants: the STOVL F-35B. This meant that the wing are could only get so big, and the airplane could only be so big, if they wanted an engine with the necessary thrust for STOVL operations. The Israelis would have preferred a stretched version, with more fuel, more payload, and two cockpits. They also would have preferred to install their own EW systems, so that they did not have to become reliant on the US to supply electronic libraries and jamming routines for the US and European-supplied radars and missile systems sold to Israel's neighbors. But they are not going to get those things, and they cannot afford to purchase enough airplanes on their own to justify launching an all-new, indigenous fighter program without a foreign partner. Whether they could do so is moot. They can't afford to do so on their own.
So for now, the Israelis are planning to buy the F-35, beginning with an initial batch of 20 fighters due to arrive between 2015 and 2017.
Israel To Buy F-35s With Cockpit Mods | AVIATION WEEK
Follow-on purchases, however, will depend a lot on the terms being offered, and what else becomes available. Contrary to popular belief, the F-35 is not expected to be the last fighter that the United States ever produces.
Boeing displays concepts for F/A-18E/F replacement