There isn't any added security for the LHR departure that is noticable. However, the Israelis are the best for airline security and you can be sure that they know pretty much everything about all passengers, probably down to inside leg measurements.

TLV can be an absolute nightmare at the best of times.

There is no fast track, but in order to speed up your entry you can book VIP services. They will meet you off the plane and take you by car to immigration, which can be up to 20 min walk. They will then take you through a seperate line. I haven't been for a while but it's around $80 per person, I think.

The only way to minimise the pain of departure at TLV is by booking in F or J. If you do then 90 mins should be plenty of time, otherwise I would suggest between 3 and 3 and a half hours. The airport security is pre-check in and the security guard won't be concerned as to whether or not you have a Gold Card. If you're ticket says F or J then they will show you through to a Fast Track line and security will take about 10 mins.

The airside shopping isn't great and the lounge is pretty poor too, but as Clubman said there is free wi-fi.