No. There is no AppleScript support for the Apple Dictionary application, or available to Pages that would allow it to grab words from the following Lookup pop-over content. The description of a manual process below may be awkward, but it does work.
When you select a word in your document to lookup, either with the control-command-D sequence, or three-finger tap on a trackpad — you get a pop-over panel organized by limited dictionary names and a brief description within each. Looks like this familiar image:


Unfortunately, none of the text on this initial pop-over is selectable for copy/paste to replace your original selected word. However, if you click anywhere within the description, the pop-over changes (second image) to focus on its content that has selectable (not clickable) words. This gives you the option to copy, click in your document body to dismiss the pop-over, and then with your original word still selected — paste to replace it.