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"I have a B&W negative jpg image of 15228kB
I run this image through Negativ lab pro
I then select File->Export
The jpg image size will then be 8901kB
How to set Lightroom to get the maximum size of the image?"

JPG supports compression which does not affect the number of pixels but the quality.

• In File Explorer, what are the dimesions of pixels when you hove over the 15228kB file
• In a similar light, what are the dimensions for the exported 8901kB file

If there is a difference, then editting done in Negativ Lab Pro changed image.

The difference in size could be caused by the compression selected on the export from Negativ Lab Pro

How to set Lightroom Classic to get the maximum size of the image?

Size of the exported JPG file is usually irrelevant. You are spending time on something that doesn't matter, and can't be precisely controlled, and not worth the time you will spend on it.

The number of pixels in the exported file is what is relevant in this case, and the visual appearance is also relevant. Do not judge exported JPGs by file size.

Q1: Why does it matter? JPEG compression algorithms are pretty good, and as long as the physical (H xW) dimensions and image quality are retained, the file size generally isn't important.

Q2: Do you have the "Quality" slider at 100%?