In 8.5.2 you can not get handle of SOAP Header in web service provider. According to Elena Neroslavskaya one can somehow extract the generated Axis code base and make the changes there. Definitely not an option for me: I do not want to extract some %%webservice.jar%% files attached to web service provider design element, make changes to files inside it and then put it back.
But I tried to get MessageContext.getCurrentContext() from web service provider in Lotus Domino 8.5.3CD5 and it seems to work!!! At least web service can be compiled without errors. Trouble is I do not have 8.5.3CD5 server installed just now and therefore I can not test it. But I think they made MessageContext available in web service provider code for a reason.
EDIT: I tried it on 8.5.3CD5 server and it works!