What you are seeing in Lightroom are the previews of your pictures. They will have an exclamation mark on the thumbnail, indicating that the original files are missing. You will not be able to edit these images until you re-connect the external drive.
Rafael I thank you for you very prompt answer to my question.
Sent from my iPhone
The previews that LR makes for itself are small and their size can be set in Preferences. The default is around 1600 pixels wide and it should be set to the size closest to your monitor resolution.
Another feature that might interest you is the ability to make Smart Previews, either at import or later. The SP is a 2560 pixels wide DNG, whereas the normal preview is a jpg, and as such can act as a surrogate for the Raw file and can be edited in place of it when the external drive is offline. When the drive is reconnected, the edits are associated with the original.