You can't use drag & drop. What you have to do to keep edits synched is setup a publishing service to your hard disk, and then import images from that publishing service into InDesign.
I drag and drop from Lightroom directly into InDesign layouts all the time. There are some restrictions, though.
1. The image must be in a file format that InDesign recognizes. If the images are raw, they must be exported to PSD, TIFF, or JPEG before they can be dragged from Lightroom into InDesign.
2. No other applications can read Lightroom image edits, so if you've made any Lightroom edits to a non-raw image you do have to export a copy to include the changes. But if you only cataloged the images with Lightroom and didn't edit them, it's OK to drag them directly to InDesign.
I don't find 1 or 2 to be very limiting. I maintain the master images in Lightroom and have an export preset for InDesign that sends them to a different folder for InDesign. The export preset has "Add to this catalog" selected, so any exported image automatically shows up in the catalog for dragging to InDesign. If I saved the export destination folder or collection in my Favorite Sources (in the Filmstrip), I just have to switch to it and then drag the exported intermediate file to the InDesign layout.
If I'm iterating between InDesign and Lightroom, each time I notice that an InDesign image needs an edit I switch to Lightroom, make the edit, and hit the Export with Previous (Preset) keyboard shortcut. That updates the exported image, and when I switch back to InDesign, the image is automatically marked as modified in the Links panel. Not too much work involved there. (If you use Johan's tip about using a Publishing Service, it will re-export for you.)
3. I do this on a Mac, and I understand that drag-and-drop does not work as well in Windows. But on the Mac, Lightroom appears to be fully compliant with OS drag and drop, so I have no problem dragging directly from the Lightroom Grid to InDesign, Premiere, or any other application that receives drag and drop imports from other applications.