Hello again,
As promised, here is a more complete description of what I am trying to achieve, screen shots included in order to make it easier to understand. I hope this will describe my issues better and assist you in resolving them.
As mentioned before, I'm building a form that is used to fill in service tickets. The list of service tickets is built into a Sharepoint list, that is stored on my Sharepoint infrastructure. I'm using Power Apps to customize the form for my users. The Sharepoint list hosting the service tickets has several columns used to store the data pertaining to the service tickets. Most of these columns are simple values, but a few are lookup columns, which are taking their values from other Sharepoint lists on the same site. These lists are basically there to reuse common information that is shared across the entire business, so they can be updated independently and not hard coded into the app.
Here's a view of the of a few of the columns that are in this service tickets SP list:

As told, some of them are lookup columns that are sourcing their data from other SP lists on the same site. These lists are being used in other applications, so I have to use them as the source of the data for the service ticket SP list but I cannot modify them.
In the Power Apps form, I'm using combo boxes (thanks @WarrenBelz )to get the data from the individual underlying SP lists:

The first combo box (cmbGlobalCustomer) is placed inside a data card (this is a canvas app that I'm modifying from the Sharepoint list "form setting" option and the data cards were placed by default by Power Apps Studio)
The data card has the following properties:
Default = ThisItem.GlobalCustomer
Update = cmbGlobalCustomer.Selected
And the combo box (cmbGlobalCustomer) the following properties:

Here, I'm having issues with which function should be favoured for the Items property: Distinct, Choices or simply the content of the SP list column? (I had that working initially but made so many changes troubleshooting that I regressed a bit).
Once the user has selected the higher level customer, I need the second combo box, which identifies the customer at a more granular level (by its location) to show the choices that are only related to the top level customer. This is to be displayed in a combo box (cmbCustomerLocation), which I filter using the Filter function:

This combo box has the following properties:
Items = Filter('Customer Location','Customer Name'.Value = cmbGlobalCustomer.Selected.'Global Customer')
Which works but for which I get a delegation warning, which shouldn't be a problem given the small size of my lists.
Again, this combo box is place in a data card.
The last combo box retrieves the "Customer name" and works exactly as the second level combo box (except that it gets its data from a the "Customer Contact" SP list).
So far, I was able to get all of these combo boxes filtered correctly, and display the proper information, but when I submit the form, nothing saves to the SP list.
The funny thing here is that I have got very similar lookup columns that are included in this list and that accomplish the exact same thing, but that were placed there automatically when I started editing the form. These work flawlessly. The only difference is that they are not being filtered.
Take a look at the following combo box:

It has its data source in another SP list called "tblApplications" with the following properties:
Items = Choices([@tblTechnicalRequest].Application)
And placed into a data card with the Update property set to DataCardValue11.Selected.
When I edit an item or create a new item in my service ticket SP list, selecting the application works and it gets saved.
Let me know if there are more information that I can provide you, and many thanks for the help you've provided so far!
Winch