Loamy soils are basically well balanced ones, with good proportions of clay, sand, and humus materials - ie good well worked garden soil. I think the nearest you can come to buying it is to get a John Innes compost mix, but it would break the bank to use it over a whole lawn unless it is a very small one. To top dress a lawn on a clay soil you would go for a sandy loam rather than a clay loam. Do you have a compost bin, as adding some coarse sand to sieved home made compost would be OK.
A good start with a clay lawn would be to spike it all over and brush some coarse sand into the holes. Then if you haven't got any loam or don't know of anywhere you can dig up some leaf mould legally, you could fall back on using a standard lawn feed.

I'm no lawn expert but noticed you hadn't had any replies. Hopefully one of the Goyers with a beautiful lawn can give you a more helpful answer.

I have exactly the same problem and shall be very interested to read other people's replies. I have made a start by scarifying the parts that need it, spiking as far as I can - after a few weeks' drought it's like concrete - and brushing in some sieved leaf mould. (we don't have much - it's like gold dust) I don't think you CAN buy leaf mould, and all our precious compost was used on flowering and fruiting plants. As soon as we have some appreciable rainfall I shall use a lawnfood, but one without weedkiller, as the lawn is more clover than grass. It is all I can think of, short of mouth-to-mouth resuscitation to bring it back to life. If it makes any sort of recovery, I might be tempted to re-seed the worst parts, but it's one step at a time. What exactly is "lawn sand"?