Lumo are one of several TOCs who have marked their trains as "reservations compulsory" in the timetable data. However, this is misleading because reservations are not actually required to travel with them. They do have some unreservable seats;
their website contains a map showing them.
That being said, Sunday morning is a very popular time to travel from Edinburgh to London, so I'd recommend getting to the station in good time - ideally in time for the train's inbound arrival from the depot, scheduled at 10:35 - to make sure you can get a seat. Otherwise there is no guarantee of being able to sit down, which would obviously make for a rather uncomfortable journey down to London.
If you're sure you want to travel with Lumo, you could buy a "Lumo only" Anytime Day Single for £75, which represents a small saving over the interavailable Super Off-Peak Single costing £87.
As there's no saving by buying either ticket in advance, and Lumo are often very poor about arranging ticket acceptance in the event of disruption, I'd recommend making the choice on the day - or using a site that makes it easy to get a fee free refund if you change your mind. Either ticket is flexible, so you can buy it simply by choosing any service that Sunday from the relevant operator.