Hi @mrmajorthorburn
Try a syringe filled with Isopropyl Alcohol 99%+ (available from electronics parts stores) and use it to run a line of alcohol along the LCD panel edge and the cover to start softening the adhesive.
It's a slow process as once the adhesive has softened you will have to gently pry the cover from the panel a bit at a time and then apply more alcohol to the next section that it still stuck and so on
When you finally have removed the cover, use the alcohol to clean the inside of the cover of any residual adhesive.
Once clean use thin double sided adhesive strips to secure it to the new LCD panel
Failing that here's a [https://www.parts-people.com/index.php?action=category&id=151&subid=367&refine=lcd+back+cover|lid/back cover parts list] that may help.
Search online for ''Dell (insert required part number)'' to find suppliers that suit you best. e.g. black cover = Dell [https://www.google.com/search?q=dell+122RP&client=firefox-b-d&sca_esv=598728132&ei=7jemZYHgGdmV4-EPoI-LgAc&ved=0ahUKEwiBj8fXuOGDAxXZyjgGHaDHAnAQ4dUDCBA&uact=5&oq=dell+122RP&gs_lp=Egxnd3Mtd2l6LXNlcnAiCmRlbGwgMTIyUlAyBRAhGKABSNgVUN0EWPoQcAF4AJABAJgBlAKgAe8IqgEFMC4yLjO4AQPIAQD4AQHCAgsQABiABBiKBRiRAsICBRAAGIAE4gMEGAEgQYgGAQ&sclient=gws-wiz-serp|122RP], red cover = Dell [https://www.google.com/search?q=dell+J1c2G&client=firefox-b-d&sca_esv=598728132&ei=4DemZfqzE_Xv4-EP0_aL8A0&ved=0ahUKEwj6o-rQuOGDAxX19zgGHVP7At4Q4dUDCBA&uact=5&oq=dell+J1c2G&gs_lp=Egxnd3Mtd2l6LXNlcnAiCmRlbGwgSjFjMkcyCBAAGIAEGKIEMggQABiABBiiBDIIEAAYgAQYogQyCBAAGIAEGKIESMhNUORFWORFcAJ4AZABAJgB4gGgAeIBqgEDMi0xuAEDyAEA-AEBwgIKEAAYRxjWBBiwA-IDBBgAIEGIBgGQBgg&sclient=gws-wiz-serp|J1C2G]
Here's the [https://dl.dell.com/manuals/all-products/esuprt_laptop/esuprt_alienware_laptops/alienware-m18x_service%20manual_en-us.pdf|service manual] that may also help.