You're probably right -- I do need to review my thermo. University was many years ago, and thermo was taught in a hot class room in the middle of summer by a prof who was in his 60s and coasting to retirement. But I meant to claim that lithium battery chemistry was thermodynamically reversible _in theory_, whereas a heat engine (such as a gasoline engine) is not. Although I'm not really sure if this is true either, but practical efficiencies are in the 90% range (according to the sources cited by wikipedia), which includes internal impedances, and other real-world losses. So it seems likely to either be theoretically thermodynamically reversible, or very close.
But you were the one who said the hydrocarbons were being burned (in your previous post). In this case, lithium battery discharge/recharge cycle is up to ~90% efficient, whereas gasoline burning has an average efficiency of 25-35%. So ignoring the efficiency of the hypothetical gasoline recovery process, that's a difference of at least 55%.
I think it's ironic that you consider a difference between 100% and 90% completely invalidates what I'm saying, but me pointing out a difference between 90% and 35% is being pedantic.