The challenge with aphids is this: even if only one remains, she can pop out pregnant babies who will have kids of their own within weeks.

So, persistence is the key. Repeat whatever you've been doing. Then repeat again.

Consider that if you use nasty chemicals, you get to eat the residue.

I would stick with periodic applications of insecticidal soap. And if that didn't work, I suggest that this is one of the hazards of winter-time growing and, possibly, stressed lettuce.

Any one Aphid has a life span of only about 30 days, but during that time can produce prodigious numbers of offspring by live birth which will also produce prodigious numbers of offspring. Very often people will use a water spray to knock off the Aphids they see and then will see more and think the ones they knocked off have returned even though they did not. As Jean stated persistance is the key to control.
Also, Aphids are more likely to be on plants with lush, green growth, often plants that are growing in soils with too much Nitrogen. Look at your soil to see if that is part of the problem.