One book that is not that well known today is Playing the Horn by Barry Tuckwell. It was written by Tuckwell in much the style of being his version of The Art of French Horn Playing.
A master of the lip trill speaks
As his recordings attest, Tuckwell was a master of the lip trill. In Playing the Horn he offers great advice and more on the topic. Starting very practical, Tuckwell notes that
…the fact is that a trill is only a rapid movement between two notes. Every player can move from one note to another and back again; however slow this may be, it is still a lip trill. The task is to try to increase the speed. There is no secret formula to produce lip trills…. The time-honoured lip trill exercises still hold good today…. Most important is to know exactly how fast to play a trill—this will always differ according to the dynamic level, the register, and the length. Lip trills are not produced by the lips alone; every note we play requires a different tension of the face muscles and a different pressure of air. Therefore it must be remember that, even in a rapid lip trill, the upper note needs more air pressure. Thus a basic physical problem of trilling is that the difficult progression, that which requires greater effort, is from the low to the high note. Here one has to think differently from the way one would behave instinctively. It is therefore of great benefit by way of contrast to practise trills starting with the upper note. A common misconception on how to practise trills is the dynamic level. If played softly the trills can frequently be respectably fast, but although this may be adequate at home it is soon found to be insufficiently loud for practical use. The amount of effort required for a loud trill is much, much greater. Therefore trills should also be practised as loud as possible.
Experiment with non-standard fingerings
Tuckwell also notes that you should experiment with different fingerings for trills, in particular fingerings that might at a slower tempo be unusable. For example a trill on written third space C might normally be fingered open on the F horn; taken as T12 “The D will be slightly sharp and the C definitely flat, but at speed the narrowing of the gap between the intervals will make them in tune.” He notes that this system may be “adopted in many places” and also that “A good half-tone [lip] trill also can be made out of a three-quarter-tone interval.”
A practical approach to camouflaging a weak lip trill
A final note from Tuckwell is again extremely practical.
A good way of camouflaging a weak lip trill is to start very slowly, finish in a slow, deliberate fashion as at the beginning, and incorporate a turn at the end. However dull this may sound, it is better than the disastrous mess that misguided over-enthusiasm will produce.
With Tuckwell we finally have some great insider information from a master! So far as I know this book is long out of print (his publication Horn is much easier to locate) and it is certainly one to look for in an academic library or among the books owned by an older horn player. Next time the series on trills closes with notes from two more recent publications.