well, LN has several modes. the default mode is to generate .xnml files only, when run in global mode. that's probably the mode you want, rather than "apply normalization".
the idea is that rather than outputting a whole new copy of the image which have been normalized, it just outputs a file that describes how the file should be normalized. ImageIntegration knows how to read this file and do the normalization internally while it is integrating the frames. the .xnml files are small in size, which is a bonus.
so what you do then is load the _c_r.xisf files (that is, the calibrated and registered files) into ImageIntegration using the "Add Files" button, then, using the "Add L. Norm Files" button, select all the .xnml files. ImageIntegration will match them all up. then you set the Normalization mode in ImageIntegration to "Local Normalization" to make ImageIntegration use the .xnml files. the nice thing here is that because you are using the same input image files, you can easily compare the results of regular normalization and local normalization just by switching the normalization mode in II and re-running.
rob