Try the performance accelerator.

When you're showing the screenshot from Google page speed score, you're only measuring front end performance. This is not the correct way to measure an App's performance. The page speed is not logging and checking the query performance where the accelerator works.

In effect an App's performance is much much more than just front end script performance. The tutorly website should be divided into 2 parts, a. Website b. App. 

The website can be fully cached out except for the app page.

The find your tutor page is loaded in 1.2 seconds thereafter it is the queries that are loading so the complete loading is taking 45 seconds but again this is not a complete measure. 

If find your tutor will have fixed set of tutors, the queries can be cached to show these results much much faster. So any object caching plugin can improve the performance of your script

https://prnt.sc/Kzij7vUHivRA

Yes but the Strategy for optimisation remains the same for WPLMS & Tutorly.

All of tutorly only works on 1 page which is the app page, the rest of the site can be fully cached.

the server specs are good, what is the peak traffic you estimate on your site.

checking this ...

1. Yes it does not have bootstrap 

2. Barebones template is not required, we have the vibe App template as a better replacement in Tutorly.

3. I understnad, we may remove the dependency on the login status in the directory to speed this up/ 

the issue here is that the calls are returning too slowly

https://prnt.sc/GlTOEaxTB7A1

I doubt  removing login.js dependency can fix this. Simply because while API calls  are running the data is scripts login.js is already loaded  up. The issue is becuase the database calls are returning slowly. 

one think you can try is removing other plugin dependency and make the rest api calls little faster. But ultimately it depends on the processing power of the server on how quickly it responds to the queries.

installing query monitor plugin and sharing further details ...

My analysis is this.

You have a good object cache system installed in your site  and it is working caching all WP reqeusts but only on page loads. The API calls are outside the page loads & thus not object cached  hence they get a large delay.

https://prnt.sc/tFSGaYAvFlBy (typo op => ob (object))

The ram consumed is pretty low like 84mb on page but the mysql query responses are slow. To improve the performance increasing mysql resource allocation, version etc is required

The API slowness is consistent with WP ajax calls from WP , https://prnt.sc/y0jqgW29Ip72

both these calls are not cached by page loads.

Hi please check the image there is something wrong with the server itself most of the things are slow even in the admin panel .

also I found installing caching plugin increased the site page speed . 

to increase mysql memory allocation : https://help.eset.com/protect_deploy_va/90/en-US/increase_memory_mysql.html

for this please contact your webhost or hosting provider.