I think it is impossible with TComboBox.
The most similar thing I found in Lazarus: Tools -> Configure Build Lazarus ... (done by THeaderControl + TListBox)
You will probably have to do it by combonation of TEdit + TListBox (and you will show/hide TListBox).
Or possibly you can use one TStringGrid or TDrawGrid and change its height (one row / more rows).
And of course you will have to draw your own icons using OnDrawItem events.
At this time I have no idea for simplier solution.