LyX Goes With Tikz

To load tikz package, just like all the other $\mathrm{\LaTeX}$ packages, try set $\mathrm{\LaTeX}$ preamble under Lyx > Document > Settings > LaTeX Preamble, put

\usepackage{tikz}

And in LyX, Press Ctrl + L to insert TeX/LaTeX code. e.g.

\begin{tikzpicture}[thick,minimum size=2.3cm]
\path (0,0) 
 (0.8,1) node (c) [circle,fill=red,fill opacity=0.5]{}
 (-0.8,1) node (b) [circle,fill=green,fill opacity=0.5]{}
 (0,-0.4) node (a) [circle,fill=blue,fill opacity=0.5]{};
\path (0,-0.4) node (a1) {$C$}
      (-0.8,1) node (b1) {$B_0$}
      (0.8,1) node (c1) {$A$};
\end{tikzpicture}

And finally, use File > Export -> PDF (pdfLaTeX).