The mileage credit situation with TP crediting to partners is a mess. This has nothing to do with it being TP mainline or an affiliate such as TAP Express or Portugalia.
Every economy fare code on TP is sold as one of four products: Discount, Basic, Classic or Plus. See TAP product line
here. No matter the booking code (M in your case) what matters to TAP is what product of M fare you bought. If you buy anyfare-Discount you get 0 miles. Even full Y-Discount would get 0 miles. If you buy anyfare-Basic you get 50% miles on UA. anyfare-Classic you get 100% miles. And I think anyfare-Plus is also 100% but have never tested. The other day I bought E-Classic and got 100% miles, even though E is a dirt cheap class and theoretically would not earn anything on UA, but I uprated the product to E-Classic and got 100% miles on UA.
At TAP, the booking code is used for yield management only, and the product class is used for ancillary services such as baggage, seat assignment, and yes, mileage earning.
This is not understood at all by UA agents. They go by booking class only, but booking class is meaningless to TAP for the purposes of mileage earning. To TAP, mileage earning goes only by the product.
If you buy directly from flytap.com is is very clear which product you are buying. If you buy from a third party, they will typically only always sell you Discount, because it's cheapest and, well, to a third party an M fare is an M fare is an M fare. But it's not. On the RAK-LIS one-way, the M fare codes are:
Discount M25DSC0B 141 EUR (+YQ +taxes) -- bare bones, no miles
Basic M25BSC0B 155 EUR (+YQ +taxes) -- gets 1 checked bag and 50% miles on UA
Classic M25CLC0B 159 EUR (+YQ +taxes) -- gets 1 checked bag, seat assignment and 100% miles on UA
Plus M25PLU0B 203 EUR (+YQ +taxes) -- gets 2 checked bags, seat assignment, priority handling, and (I think) 100% miles on UA
What you have to look for are those characters DSC / BSC / CLC / PLU in the fare basis. That is what will determine your mileage earring. The common consumer does not know this.
I know, this situation is not explained like this anywhere on the UA site. And UA agents don't know about it. But it is what the reality is. If you want miles when flying TP, upgrade your product on TAP -- which means you probably have to book directly with TAP.
You could argue with UA agents as much as you want, TAP will not grant the miles for a DSC product. If you ever get miles, it will be because UA gave them to you out of the goodness of their heart.
Now, all the above applies to TP fares, which I assume if what your RAK-LIS was. If you fly TP on someone else's fare (e.g., you fly ORD-LHR-LIS on a UA fare, with the LHR-LIS segment operated by TP) then indeed the TP booking class as shown on the United earning table is what rules.