Can you extend the life of frying oil with lettuce?
With regard to your source that suggests adding lettuce will reduce foaming of the oil: it might be possible to use lettuce as a tool to scoop up surfactants from the surface of the oil. If you're going to attempt it, I think the best time to do it would be when the oil is cool.

An Introduction to Surface Tension

Foaming is related to surface tension: for example, adding a surfactant (such as soap in water) to a liquid reduces its surface tension, which makes bubbles more stable. So to reduce foaming, you would need to increase the surface tension.

Note that we can't increase surface tension by adding something to the oil: the only way to increase the surface tension of a liquid with an additive is to increase its overall density.

To see why that's the case, suppose for a moment that there were a magical substance that liked to stay on the surface of the liquid and caused higher surface tension. That higher surface tension would compress the liquid, and raise its pressure. That means any spot on the surface that had less of the substance would have less surface tension and less pressure, so the pure liquid would be pushed out of that spot and cover the surface. That process would result in the substance never actually being on the surface of the liquid, which contradicts our starting assumption, so no such substance can exist. Instead, such substances become distributed evenly throughout the interior of the liquid...and, if they make the liquid more dense, that raises its surface tension.

So, if we want to increase the surface tension of aging oil, the only way we can do that is by removing surfactants from the oil, assuming we don't want to mix the oil with large quantities of something more dense.

Surface Tension and Frying

As J. B. Rossell explains in Frying: Improving Quality (with credit to BaffledCook for finding the source), surface tension is very important in deep fat frying, beyond just the idea of foaming.

Initially, oil for deep fat frying tends to undercook (or takes longer to cook) food, because few surfactants are present in fresh oil. Due to the high surface tension, the oil is less often in direct contact with the food being fried (as little as 10% of the time it is submerged), which means less heat transfer by conduction, less of a crust, and less oil present in the final product.

As the oil gradually breaks down with repeated cooking, surfactants build up in the oil, reaching an ideal range which gives the preferred golden crust and moderate greasiness, with oil being in contact with the food between 20% and 50% of the time it is submerged.

When the oil goes bad, the high quantity of surfactants results in too much contact between the oil and the food, resulting in greasy food that is overcooked on the outside and undercooked on the inside, and may have a bad flavor due to the rancidity of the oil, or contamination from the food being fried.

Removing Surfactants

First of all, I want to say that I'm not sure I'm in favor of trying to prolong the life of frying oil beyond its natural lifetime: the breakdown of the oil results in potentially cancer-causing free radicals, so I'd rather err on the side of replacing the oil too often, especially if I'm cooking for myself or loved ones.

If you were going to re-use the oil anyway, you might be able to reduce the amount of oil that gets into your food by reducing the quantity of surfactants, but if you're debating saving money by using your fry oil longer than you normally would, I'd say a bottle of oil is cheaper than a trip to the oncologist's office.

Speaking of cost, I think a bottle of most oils used for frying is also cheaper than a head of lettuce, so I'm not sure how economically viable this strategy is.

That said, since surfactants (SURface ACTive AgeNTS) are attracted to the surface of the liquid (they find a lower energy state by decreasing the energy of the boundary between two liquids or a liquid and a gas), they can potentially be removed by skimming (or just pouring) them off the surface. (I expect putting the oil in a narrow bottle and pouring off some of the oil from the top would be a more economically viable solution to remove surfactants.)

Because crinkly lettuce leaves have a high surface area, its possible that just dipping lettuce in the oil and drawing it out might remove a significant amount of surfactant, especially if the surface area of the lettuce leaf is high in comparison to the surface area of the pot that the oil is in: the surfactant will attempt to spread evenly across the entire surface of the oil. If we assume the surfactant is attracted only to the oil/air boundary (note: I have no knowledge of whether this is actually the case, or whether the material of the container matters), then when a lettuce leaf with a surface area equal to the surface area of the oil/air boundary is dipped into the oil, and then slowly removed, the oil covering the top of the pot and the oil covering the lettuce leaf will have roughly equal surface area, and if the surfactant has had time to spread evenly, they will have roughly equal amounts of surfactant, so dipping the lettuce leaf in once and removing it would remove about half of the surfactant (though somewhat less, due to dripping returning some of it to the pot).

Drying the lettuce leaf (or taking another similarly sized leaf) and repeating would drop the amount of surfactant to about 25% after the second attempt, around 12.5% after the third, etc.

Using a pot or bottle to hold the oil that reduces the surface area would make it more effective: if the ratio of surface area between the oil and the lettuce leaf were 1:2, you'd be removing two thirds of the surfactant each time, but if it were 4:1, you'd be getting at most 20%, and it would take a lot of dipping cycles to make any noticeable difference. If (as assumed above) the surfactant is present only on the oil/air barrier, then a tall thin pot or bottle would be ideal; if instead the surfactant spreads over all surfaces of the oil (including the oil/pot barriers), then it'd be best to put it in a pot that makes the depth of the oil fairly close to the width of the pot.

Of course, anything with a high surface area would be a good candidate to remove surfactants via this dipping method, there wouldn't be anything magical about lettuce leaves beyond their shape (and perhaps their affinity for oil), anything with a high surface area that doesn't immediately shed all the oil as its pulled out would work just as well.