If you are using the Lua graph drawing facilities, why not use the graph syntax?
\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{graphs,graphdrawing}
\usegdlibrary{trees}
\begin{document}
\tikz\graph [binary tree layout] { a -> {b, c}};
\end{document}

To style the edges, you can just add the information to the specification for the graph. For example:
\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{graphs,graphdrawing}
\usegdlibrary{trees}
\begin{document}
\tikz\graph [binary tree layout, edges={thick}] { a -> {b, c}};
\end{document}

Note that if you prefer to specify the diagram using the standard node/child syntax, then you are not really making use of the graphs library, although you could still use the graphdrawing library (see below). In that case, it might be easier to just drop the binary tree layout and specify the shape the tree will take yourself. In this case, just drop the graphs and graph drawing stuff:
\documentclass[tikz,border=10pt]{standalone}
\begin{document}
\begin{tikzpicture}[
edge from parent/.style={draw, ->, thick},
]
\node {a}
child{node {b} }
child{node {c} }
;
\end{tikzpicture}
\end{document}
for very similar output:

You can also use the graphdrawing library with the more standard syntax. In that case, you can apply a style to the edges using every edge/.style={}. However, specifying -> apparently has no effect:
\documentclass[tikz,border=10pt]{standalone}
\usetikzlibrary{graphdrawing}
\usegdlibrary{trees}
\begin{document}
\begin{tikzpicture}
[binary tree layout, every edge/.style={draw=blue, thick, ->}]
\node {a}
child{node {b} }
child{node {c} }
;
\end{tikzpicture}
\end{document}

Presumably there is some workaround for this, but my brief experiments did not discover it.
->is ineffective in the last tree. – cfr Oct 21 '15 at 20:35\graphcommand? – MaxNoe Oct 22 '15 at 14:05graphsandgraphdrawing. I thought I did, but I think I thought wrongly. – cfr Oct 22 '15 at 19:29binary tree layoutunless I also specify some further stuff using e.g.every edge. – cfr Oct 22 '15 at 20:57