Movies which have twists especially the shocking ones are appreciated by thriller buffs. Memento is so twisted that because of its unique unforeseen non-linear narrative it doesn't really need a great twist in the end--still like all great thriller mysteries which seem solvable to an audience--it has a surprise twist in the end. I have watched it many times and read many reviews--still, following is what I feel I consider is the 'gist' of the clues to understand the mystery of this story. Though I feel that a Mystery can never really be known truly---objectively---but you're free to interpret and enjoy the interpretation---this doesn't mean however that it's the only interpretation possible!
I am convinced that though not absolutely clear..still if you believe that clues lie in the film( as once Nolan pointed out!) you've to build your interpretation on the clues you see in the film. The most reliable source of information is Teddy and not Lenny--because if Teddy is not reliable there's no other source at all. It's clear though, that Teddy is using Lenny for his own gain--because he's a snitch(undercover) as well as a drug dealer(corrupt cop)--Teddy has already given Lenny a John G whom he killed but continued killing...just to have a purpose to live...and you see an image in the very end where Lenny's wife is lying with him and he has tattoos on his chest--which means he had started searching for John G even when his wife was alive. So as Teddy said 1. Sammy Jenkis had no wife.( This makes me feel that Sammy was a person with a similar condition) 2. Lenny's wife killed herself out of desperation and Lenny overdosed her...which obviously means...as Teddy said 3. Lenny's wife had survived the attack. 4. Lenny removed 12 pages from the complete police report of the incident in order to continue the manhunt in the fashion similar in which he makes Teddy the target in the end.
The John G was killed because after killing Lenny took a photograph in a good mood---though you might contest this by saying: why there's no note on that photo---obviously because somehow Lenny didn't want to end his "mission" in the past...similar to as he didn't want to end it even after having heard what he feels is Truth from Teddy( Here important is "instincts"---you can easily infer that while discussing with Teddy in the last scene...as he looks at the photos and hears him out...he "feels" that it's Truth...that's why he burns the photographs.)---It's evident with these things that he's just starting another cycle of killing and he'll continue killing many more people...he's the most immoral person...even more immoral than Teddy is in this picture. Still, I feel that there's no absolute interpretation possible for this film--I find that many objections might be raised against my interpretation above. What a superb masterpiece it's--Nolan broke the tool with which he created it after its creation methinks!
image source: here