HP rings a bell
Several HP computers with the same and similar age as your computer do not 'want to' boot via grub, if there is a GUID partition table, when accessed via USB. If there is an MSDOS partition table and the boot partition has a boot flag, it works. (Normally booting via grub should not bother about the partition table or boot flag.) My son and some friends have such computers, and I have tested and verified this behaviour more than once.
You can check the partition table with the following command
sudo parted -ls
Unfortunately dd_text_16.04-UEFI-n-BIOS_2017-05-07_intel-4-pendrive-7.8GB.img.xz has a GUID partition table.
Modell: SanDisk Extreme (scsi)
Disk /dev/sdd: 16,0GB
Sektorstorlek (logisk/fysisk): 512B/512B
Partitionstabell: gpt
Disk Flags:
Nummer Början Slut Storlek Filsystem Namn Flaggor
1 1049kB 316MB 315MB fat32 startbar, esp
2 316MB 317MB 1049kB bios_grub
3 317MB 7262MB 6946MB ext2 root
4 7262MB 7799MB 537MB linux-swap(v1)
Test
But I think it will work for you from the following image, dd_Lubuntu_16.04.2_amd64_persist-live_mkusb-12.1.4_7.8GB_msdos-pt.img.xz. It has the correct partition structure to boot also in 'middle-age HP computers'.
Modell: SanDisk Extreme (scsi)
Disk /dev/sdd: 16,0GB
Sektorstorlek (logisk/fysisk): 512B/512B
Partitionstabell: msdos
Disk Flags:
Nummer Början Slut Storlek Typ Filsystem Flaggor
3 2097kB 130MB 128MB primary fat32 startbar
4 130MB 1072MB 942MB primary
2 1072MB 6443MB 5372MB extended lba
5 1073MB 6443MB 5371MB logical ext2
1 6443MB 7799MB 1356MB primary ntfs
In linux you install from compressed image files with mkusb. In Windows you can use Win32 Disk Imager.
Final installation
I remember that you don't want a persistent live system, but if you test it and it works, you can create an MSDOS partition table with the relevant partitions and flags in your USB stick. gparted
is a good tool for this purpose.
Then you can install Ubuntu into it with Ubuntu's standard installer. It is easiest, particularly in UEFI mode, if you disconnect (unplug) the internal drive.
Select 'Something else' at the partitioning window of the installer. The target USB stick will be seen as an internal drive, when booted from another USB stick, and the installer will install the EFI boot files into it. (Otherwise the EFI stuff will be written into the internal drive and you have to copy it manually, which is possible but tricky.)
Tweaks
This link describes some tweaks for the installed system.