The package iwona sets the math fonts in a way that's incompatible with fontaxes, which is required by libertine. The warning does not depend on the class, as it shows also with the article class as soon as one issues
\boldmath
which llncs.cls does when section titles are typeset.
You get the same result, with no warning or error, by defining directly the math fonts as done in iwona.sty, with the necessary small changes.
\documentclass{llncs}
\usepackage{libertine}
\DeclareSymbolFont{operators} {OT1}{iwonam}{m}{n}
\DeclareSymbolFont{letters} {OML}{iwona}{m}{it}
\DeclareSymbolFont{symbols} {OMS}{iwona}{m}{n}
\DeclareSymbolFont{largesymbols}{OMX}{iwona}{m}{n}
\SetSymbolFont{operators} {bold}{OT1}{iwonam} {b}{n}
\SetSymbolFont{letters} {bold}{OML}{iwona} {b}{it}
\SetSymbolFont{symbols} {bold}{OMS}{iwona}{b}{n}
\SetSymbolFont{largesymbols}{bold}{OMX}{iwona}{b}{n}
\DeclareMathAlphabet{\mathbf}{OT1}{iwona}{bx}{n}
\DeclareMathAlphabet{\mathsf}{OT1}{iwona}{m}{n}
\DeclareMathAlphabet{\mathit}{OT1}{iwona}{m}{it}
\DeclareMathAlphabet{\mathtt}{OT1}{iwona}{m}{n}
\SetMathAlphabet{\mathsf}{bold}{OT1}{iwona}{bx}{n}
\SetMathAlphabet{\mathit}{bold}{OT1}{iwona}{bx}{it}
\begin{document}
Hello
$\sin\pi=0$
{\boldmath$a+b=c$}
\subsection{Hello}
\end{document}
However, text in Linux Libertine and math in Iwona is a real punch in the eye.
llncs.styis a LaTeX2.09 style, not a class, and doesn't work with\documentclass. If I downloadllncs.clsfrom the Springer website and run your example I do get the message: I guess this is what you meant? As the class is for a publisher, I'd be very wary of making any font changes or indeed loading any packages you do not absolutely require. – Joseph Wright Sep 24 '14 at 06:08articleclass as soon as one tries to do{\boldmath$a$}. Theiwonapackage is not compatible withfontaxesthat's required bylibertine. – egreg Sep 24 '14 at 10:10llncs.cls, so I guess I just haven't been using both math.) – Roly Sep 24 '14 at 10:15