MacBook Air A1370 boots directly into Lubuntu – Option key will not open Startup Manager

The safest approach is to avoid erasing or repartitioning the internal SSD for now.

On an Intel-based Mac, Apple documents Option (⌥) or Alt as the key that starts Startup Manager. 

Apple also documents Command-R for Recovery, Option-Command-R and Shift-Option-Command-R for Internet Recovery, and D for Apple Diagnostics. (Apple Support)

I would therefore first shut the Mac down completely and test Option, Command-R, Option-Command-R, and D separately. 

If Option does not produce Startup Manager, try the same test with a simple wired USB keyboard. 

Apple recommends the built-in keyboard for a Mac laptop, but also specifically suggests trying a wired keyboard when necessary. 

Apple notes that the Mac may take a few seconds to recognize a keyboard during startup. (Apple Support)

The fact that Lubuntu boots normally does not by itself show that GRUB, the GPT, or the EFI System Partition is responsible. 

Similarly, the fact that the Mac does not display Startup Manager does not by itself establish a hardware or firmware fault. 

These possibilities should be distinguished by testing the other startup-key combinations before modifying the disk.

You can safely inspect the Linux disk configuration from Lubuntu with:

sudo parted -l

lsblk -f

sudo efibootmgr -v

For now, use these only for inspection; do not delete EFI entries or repartition the drive.

It is also worth determining the exact Mac model before deciding which version of macOS to install. 

A1370 identifies the enclosure/model family, but the exact MacBook Air model identifier determines macOS compatibility. 

Apple lists the MacBook Air (11-inch, Late 2010), identifier MacBookAir3,1, as supporting macOS High Sierra, while the Mid-2009 model, MacBookAir2,1, supports OS X El Capitan. (Apple Support)

From Lubuntu, you can obtain the model identifier with: sudo dmidecode -s system-product-name

If Command-R or Option-Command-R successfully starts Recovery, that would give you another route to reinstall macOS without relying on the El Capitan USB. 

Apple's Recovery environment includes Disk Utility and the option to reinstall macOS. (Apple Support)

The most useful Apple references for this situation are Mac startup key combinations and How to start up from macOS Recovery.

In short, test the built-in keyboard and then a wired USB keyboard, try the Recovery/Diagnostics combinations, identify the exact Mac model, and inspect the disk before making any changes. 

There is not enough evidence yet to conclude that the Linux installation or the SSD's GPT/EFI structure is causing the problem.

Lubuntu is not the problem here. And any USB installer is currently irrelevant if you cannot access the Option Boot screen to show the Apple boot picker menu. This is all controlled by the hardware, firmware, and PRAM settings.

When you performed the PRAM Reset, did you hear the chimes? If not, then the PRAM Reset was not successful....you need to hold it for at least three chimes on these older Macs.

Make sure you hear the startup chime before pressing any special startup keys. In fact, press the special startup keys immediately after hearing the startup chime. Pressing/holding the keys too soon or too late will cause them to be ignored.

Try both the built-in keyboard and an external wired USB keyboard. It is possible that your built-in keyboard has a hardware problem that could be preventing the keys from being properly recognized (even on the external keyboard).

FYI, the MBAir A1370 designation refers to either a MBAir 11" (Late-2010) or (Mid-2011) model....both of which support macOS 10.13 High Sierra. You should be able to access Internet Recovery Mode using Command + Option + R to access the online High Sierra installer (certainly for the 2011 version, but I think the 2010 model as well). This won't really matter if you cannot access the Option Boot screen.