Automatically mount partitions in Linux Lite

[DeepThought]

Device    Boot    Start      End  Sectors  Size Id Type
/dev/sda1  *        2048 146485247 146483200  69,9G 83 Linux
/dev/sda2      146487294 976771071 830283778 395,9G  5 Extended
/dev/sda5      146487296 732422143 585934848 279,4G 83 Linux
/dev/sda6      732424192 771483647  39059456  18,6G 82 Linux swap / Solaris
/dev/sda7      771485696 976771071 205285376  97,9G 83 Linux

I've made the partitions during installation

From the first quote I can work out that sda1 is your root partition and sda6 is the swap partition, but no idea what the other partitions are for.
Firstly, while sda1 is a primary partition, sda2 indicates you created a logical partition and sda5, sda6 and sda7 are in that extended/logical partition. While sda5 OR sda7 is your home partition I've no idea what the other partition is for.

So based on the second quote, when you created the partitions during the installation, did you set their mount points, if you did not, that is why they won't mount automatically on boot.

You could use settings/Disks ... click on the individual partitions and then the cogs under the partition on the right, then click on edit mount options to try and fix things

OR

Reinstall and when creating the partitions, set the correct mount positions

Hope this helps