My homemade lemon liqueur stays clear while the commercial version is cloudy — what produces the cloudiness?

It is not dairy. The cloudiness in the standard version is an emulsion of citrus oils, and the effect has a name: louching.

The oils in lemon peel dissolve readily in strong alcohol and are essentially insoluble in water. While the infusion is at high strength they stay in solution and it looks clear. When you dilute it with sugar syrup, the alcohol concentration falls below the point where the oils remain dissolved, and they come out as microscopic droplets suspended through the liquid — which scatters light and gives that opaque creamy look.

This is the same phenomenon as certain aniseed spirits turning white when water is added, and it is a genuine physical transition rather than an additive.

So if yours stays clear, one of two things is happening: not enough oil was extracted, or the final alcohol strength is still high enough to keep it dissolved.

Which gives you two things to change, and they are both about the extraction rather than the finish.

Use the strongest alcohol you can get. High-strength neutral spirit strips far more oil from the peel than a standard 40 percent spirit does. This is the single biggest factor and it is why the traditional method specifies it.

Peel thinly and use plenty of it. Only the coloured zest carries the oil. White pith contributes bitterness and no oil, so a thin peel and a generous quantity of lemons is what gets the yield up.

Steep long enough for the alcohol to work — several weeks is typical — and keep it out of light.

Then when you dilute with syrup, the drop in strength does the rest by itself. If you have extracted well, the transition is dramatic and happens as you pour the syrup in.

One practical note on the peel: an unwaxed fruit makes a noticeable difference, and washing waxed fruit in warm water first helps if unwaxed is not available.

The wax coating sits exactly where the oil is, and it both blocks extraction and contributes nothing good. Whichever fruit you use, a scrub in warm water before peeling costs a minute.

On the dairy version: it is a real and separate product rather than a shortcut to the same thing.

The cream version is its own style — richer, sweeter, genuinely opaque from the milk fat, and shorter-lived because it now contains dairy and needs refrigerating.

So substituting milk into your syrup would not fix your problem, it would make a different drink. Worth doing deliberately if you want that one, and it will not get you the classic appearance.

There is also a middle case worth knowing: some clear infusions turn cloudy when chilled and clear again when warmed, because temperature affects solubility too. If yours goes slightly hazy in the freezer, that is a sign you have some oil in there and are close.