Ubuntu – Lubuntu root size

There is no "best" partitioning scheme. It really depends on your usage. E.g. if you're running a MySQL database, you might want to create a dedicated /var/lib/mysql partition for it.

10GB swap seems excessive and only useful if you need hibernation. 1xRAM + 2GB = 7G looks enough to me. The 2GB is actually used for swapping. You can lower it even more if you do not need swapping.

I've considered LVM for a regular system, but it's not worth it. Even if you can save space by it (by increasing/ decreasing logical volumes), recovery on mechanical failure/ power loss/ crash may be harder. If you've a big disk which will be unused for the big part, stay away from LVM since you do not need the extra space.

The only reason why you want to use LVM is in conjunction with LUKS (cryptsetup; a way to encrypt a partition). Since a LVM partition can hold more partitions, it'd save you from entering a passphrase for each partition because one LVM partition is encrypted, not the logical partitions in it. Of course, this advantage will only be available if you've a setup like "disk - LUKS - LVM - partition" and not "disk - LVM - LUKS - partition".

It's difficult to know these things in advance, of course, so even with the best planning you may need to make adjustments later. However, I'd recommend the following:

You won't likely need a swap partition larger than 8 GB. You have room for it and it won't hurt, but it doesn't make much sense, either, so if I were you I'd keep /swap at 8 GB.

I've had my root partition at 30 GB for about a year, and I'm still using less than 10 GB of it. You might install larger programs than I do, so give yourself a buffer: I'd recommend 20 - 30 GB.

As for the /home partition, that's where you'll store your data and files, including pictures, videos, projects, etc., whatever sorts of things you store and keep. I don't what sorts of things you keep, but in my case my pictures take up perhaps the largest share. Even so, having given myself lots of room (about 300 GB for /home), I have used only about 50 GB. You'll have to decide for yourself, but since you'll use a large NTFS partition to share data with Windows, you can probably get away with 30 - 60 GB for /home, with the knowledge that you might make adjustments later.

As far as space for Windows and its apps, etc., if you think you need 150 GB then that sounds fine. And the rest NTFS to share? That's fine, too. (Eventually you might want to revise that, but it's certainly fine at the beginning.)

You didn't say whether or not you already have Windows installed on the drive, but I assume you do. Windows can sometimes get finicky when being resized. I would recommend resizing your Windows partition first from within Windows itself using the Windows administrative tools, and then you can create the Ubuntu partitions as you install it.