AnGi;
It is not easy to provide a list of UK MIL engine related crashes in LYNX because it seems that the data is obscured. Your friend was killed in one, those nice chaps were killed in Afg, some other nice guys hit the water (both engines shut down, for some odd reason). Many ex-lynx drivers have told me of their accidents and close shaves. They don't appear to be documented.
As I say, laughable posts!
1.The outcome would have been worse if it was single engined.
"Crashed on emergency landing after cockpit had filled with smoke. Caught fire and burnt."
2. Cause not yet known.
3. The 'for some reason' the engines shut down was because they ran out of fuel having been misdirected on the way back to 'mother'.
"During Exercise Marstrike05 is was misdirected back to HMS Nottingham. It ran out of fuel 41 miles from the ship and made a controlled ditching alongside MV Wilhelm Schulte in Indian Ocean 120 miles off Oman. It sank in 2,800 meters of water but the crew were rescued safely"
Aviation Safety Network > ASN Aviation Safety WikiBase > Lynx
It is possible to find a Gazelle fatal due engine, but you have to go a long way back in time and far out in geography.
A long way back (2011 fgs!), but not as far back as your Lynx examples, and with you mentioning Lynx incidents in Afghanistan & the Indian Ocean, how does Geography affect this discussion?
ASN Aircraft accident 20-AUG-2011 Aérospatiale SA 342L1 Gazelle L611
ASN Aircraft accident 19-JAN-2010 Aérospatiale SA 342K Gazelle CN-AIP
Etc
Aviation Safety Network > ASN Aviation Safety WikiBase > Gazelle