Well yes, it is do-able - in the sense that it is a valid Oneworld Explorer itinerary.
But you have some punishing segments in there, especially travelling in economy - BUD-LHR-LAX-BNE
You do realise you can have stopovers everywhere, right?
You are allowed up to 16 flight segments, you are using only 8!
Your outbound transit in LHR is right on the minimum connect time allowed (1:30)