Once you open the Lightroom >> Go to File menu >> look for the option "Import a Photoshop Elements Catalog.."
And I think that's what you looking for.
Let us know if that helps.
You would need to install LR CC on the W7 machine if it meets the minimum requirements. Then convert the PSE10 catalog. Then move the images and LR catalog to the W10 machine.
The alternative is to select all the images in Organizer and write the metadata into the files. You could then do a straight import into LR on W10 and if most of your photos are jpegs, your keywords and captions should be recognized. But you would need to re-create any albums manually as new collections.
I converted 20 catalogues from PSE 9 into LR6 from win 7 32 bit into win 10 64 bit. I tell you my workflow which you might find useful:
I made a backup of each catalog with PSE9 on win 7-32 bit. Then I got a demo license of PSE 14, installed that in win10-64 bit and restored everything there (also moving the original images from the backup into a new PSE catalog folder (and not where they were, because that may clutter your C drive).
Then I verify everything in PSE 14 and imported that PSE 14 catalog into a new LR catalog. LR knew about all of them because they were "fresh" and both versions were up to date.. That also preserved all collections and sort-orders. I think it was not possible to move negatives during the PSE to LR import process. I then created still another LR catalog and moved the first "PSE into LR catalog" into that again but this time I moved all the images into a dedicated folder. So before I had a PSE mess with images all over the place, and now they are all in one folder accessed by a LR catalog.
(I also converted my win7-32 disk into a VHD and attached it to Hyper-V in Win10-64 to make sure I could still access everything with the old PSE9, just in case...)((you need a second Windows license if you do that for longer...))