Today it is possible to write IPA phonetic symbols by keyboard in the special IPA-mode. But therefore you have to know what symbol is on what key. And I'm not sure, if really all symbols are available there. I think it would be a great idea to have a toolbar with the IPA phonetic symbols; similar to the toolbar with the greek alphabet. So that the user can click on them to type them. They should be grouped (with a vertiacl line between the groups) by consonants, vowels, suprasegmentals,... And the order in these groups should be the official order (e.g. in consonants first all plosives, then all nasals, then trills,...)
For an overview of all needed symbols and their categorization see e.g. http://web.uvic.ca/ling/resources/ipa/charts/IPAlab/IPAlab.htm or http://weston.ruter.net/projects/ipa-chart/view/keyboard/ I think, it would be a great improvement of LyX if it has such a toolbar that the use can display when needed. Carlos