For the past 19 years I've lived in the US on E-2 Visa status and have entered numerous times, however always on a return ticket issued in the US. Now I'm trying to book a one-way from LHR.

1. Will I encounter problems checking in with my carrier at LHR, my point of departure/origin ?
2. Will I encounter problems with US Immigration at my point of entry ?

Any helpful answer is much appreciated !