If the LoadRunner is not able to record the request by itself, then you need to add it manually. I suggest you to explore Advanced options in Recording Options.
Press Ctrl + F7, click on Advanced under HTTP Properties, then click on Headers button. There you can see list of headers to check/uncheck.
If above option not working, dont use Fiddlerm because LR has built-in Fiddler engine, so use browser developer tools and trace the network log. There, you can catch all the requests and responses.