There is a longstanding view amongst a lot of people that unless an operator is listed as a "participating operator" on the relevant NRE rangers & rovers page, the rover isn't valid on their services.
I don't agree with that view. NRCoT condition 13 states that:
Your Ticket may show that it is valid only on certain train services, such as those of a particular Train Company, or on trains travelling via a certain route or routes. If no
specific route or Train Company is shown, then (subject to any time restrictions for the type of fare you have purchased) it will be valid on:
... And then it lists all the usual permitted route rules for point to point tickets. It goes on to say:
If you are using a Zonal Ticket, which allows travel within a defined geographic area, you may travel on trains which take any route within the zone or zones shown on the Ticket
Whilst this doesn't
explicitly say that you can use any operator on a ranger or rover unless the ticket says otherwise, it is clearly the implied position. The wording for point-to-point tickets is that you may use any operator if your ticket doesn't say otherwise, and the wording on zonal and geographic tickets does not contradict or limit this.
Therefore my view is that the TOC restrictions would need to be stated on the ticket to be effective.
Moreover, Lumo isn't a Penalty Fares operator and indeed I believe that buying onboard is officially allowed on their services - so the biggest risk is being asked to pay for a new (Lump only) fare and then potentially disputing that through customer services. That's a potential risk I'd be willing to take, though I recognise not everyone would be.