Internet Archive has digitized microfilm reels of various newspapers published in Lowell Massachusetts during the years of 1837-1893 including The Lowell Courier, The Lowell Daily Courier, Lowell Daily Journal and Courier, and the Lowell Advertiser.
Unfortunately, there are missing issues, and mutilated, missing, and illegible pages. This is currently the only online collection of these papers that I have found.
According to Worldcat, a couple of libraries in Massachusetts own some microfilm copies of the Lowell Courier:
According to the Library of Congress, Directory of US Newspapers, the American Antiquarian Society, Worcester, MA, holds some issues:
Online Lowell Newspapers - 1837 to 1893