TL;DR - for almost all cases, all trains which permit seat reservations need to be with the same TOC to get a cheap deal
Advanced Purchase tickets on their own are always for specific trains. When you get your ticket, it'll have 2+ parts, one for the route, one saying what trains you have to take (and normally your seat too).
In some cases, the ticket will be an Advanced Purchase & Connections ticket, which allows you to travel on "local" trains at one or both ends of your Advanced Purchase ticket. Not all AP tickets have a +Connections option though, and it tends to only be certain stations that it's offered for.
Next thing to know - on the backend side, there are two kinds of UK train tickets. There are ones valid on any operator, for which the ORCATS system shares the revenue between the different companies who's trains you could take based on seats+trains, and ones valid for only one operator, for which on that operator gets the ticket cash. Secondly, within certain bounds, normal ticket prices between any two stations are priced by a single operator, even if multiple operators might have trains on the route. For example, Oxford to Reading is set by FGW, even though you can pick between FGW and XC trains on that route.
Advanced Purchase tickets are restricted to specific trains. If all of those trains are with the same company, then that TOC can keep all the money. If it's a with connections one, then they'll need to share some of it, which they'd rather not do on a cheap ticket.
So, from Reading to Lancaster, you hit a problem. From Reading north to about Wolverhampton, ticket prices will be set by XC (Cross Country). From Wolverhampton north, that'll be set by VWC (Virgin West Coast). For a Reading to Lancaster complete ticket, they're also set by Virgin West Coast as shown here. While both companies can offer Advanced Purchase tickets for the whole route, they'll have to share the revenue for a fair bit of the ticket, so they won't price it so keenly, and probably won't release very many seats for the "& Connections".
If you book a Reading to Wolverhampton AP ticket (either on a direct train, or one with a change in Birmingham, but either way on only Cross Country trains), then XC will keep all the cash, so will have a good price, and a fair number of cheap tickets available. Likewise, Wolverhampton to Lancaster will be all VWC so they'll do cheap APs.
There are actually Reading to Lancaster AP&Connections tickets defined, for between £21 and £83.40, but for the reasons above they'll probably be hard to find. If you book just when tickets go on sale (normally 90 days out), you might manage to snag one. Otherwise, later, you'll find it easier to get TOC specific non-connections AP tickets with splitting at TOC boundaries, as they tend to have more seats available.
Oh, and another thing to consider - an off-peak single from Reading to Lancaster via Banbury (not via London) is only £49.30, so outside of peak times you'll need to play around a lot with AP tickets to get one cheaper than a flexible ticket!