mspiff When I was going through the rescue boot thingy, it seemed I was attempting to mount the wrong part and getting can not find target messages (just as a guess. I really don't know what I did wrong or right).
As a procedure, what I ended up doing was destroying all the partitions (including the the efi one) to get a complete raw unformatted disk, formatting it using ext4 (don't forget to verify you are using GUID Partition Table [gpt]), and then running the install.
After the install (supposing it went smoothly), IF you need to boot back into the live USB to do a rescue boot, you can look at the partition structure for your drive using what ever utility is used for your distro. It should be in three parts (efi, swap, and the OS). If you see three, you are probably on the right track.
When you are looking at the output from lsblk, pay more attention to the structure and position than labels. In my example:
root@solus /home/live # lsblk
NAME MAJ:MIN RM SIZE RO TYPE MOUNTPOINT
loop0 7:0 0 1.9G 1 loop /run/initramfs/
loop1 7:1 0 7.5G 1 loop /run/rootfsbase
loop2 7:2 0 7.5G 1 loop
└─live-base 253:0 0 7.5G 1 dm /run/media/live
sda 8:0 1 14.7G 0 disk
└─sda1 8:1 1 14.7G 0 part /run/initramfs/
sr0 11:0 1 1024M 0 rom
nvme0n1 259:0 0 953.9G 0 disk
├─nvme0n1p1 259:1 0 489M 0 part
├─nvme0n1p2 259:2 0 3.7G 0 part
└─nvme0n1p3 259:3 0 949.7G 0 part
the bootloader was at nvme0n1p1 and the OS at nvme0n1p3. I think the biggest hiccup is understanding what you are seeing listed (and it would be nice if someone brokedown what all the parts are from the above) so you know what the commands are actually affecting.
Or mounting different parts at random, seeing what the result is, and working out the structure from there (what I ended up doing. Will require SEVERAL reboots to the live USB.).
Once you have the parts identified, you can go through boot rescue knowing what you are affecting rather just copying commands and hoping for the best.