Did Eugene lie to save Abrahams life?

I think Eugene is very smart (as he so modestly keeps saying) & towards the end of the mid-season - Tara has been an integral part of this - he realised that lying & sabotaging the mission constantly was not going to work forever.

He was actually quite brave to admit the lie - and face the wrath of Abraham - I wouldn't want to be on the wrong side of that guy! But, there's a reason he admitted it. Was it just that he wanted to be upfront & couldn't live with the lie any further, or something else?

I know that the obvious part of the lie was self serving as it gave him importance, and instant bodyguards, however was the initial motivation to save Abrahams life? Eugene saw Abraham with the gun in his mouth ready to end it when he walked across calling for help, it was blindingly obvious he was about to commit suicide. Was that the initial motivation for the lie? Abraham had a reason for living since that point & it worked in Eugene's favour of course.

Also, Eugene may not seem to be that great with the Walkers however he had survived up until that point. He was calling for help but really didn't seem to be in a real panic. Is he actually capable?

He's a really interesting character & has strangely calculated motivations for everything he does. Seemingly thinking ahead with everything the group does & comes across.

I'm really interested to see what the rest of the season brings for this character.