That's a good question. First, I note that the "EPO" terminology seems more common among the forecast community than in the research community, where I think the EPO is closely related to the more commonly referenced North Pacific Oscillation (NPO). The studies I have seen generally suggest a tenuous relationship between La Nina and the NPO/EPO (like here), but at least one study suggests that the recent eastward shift of the NPO and increase in winter extremes associated with the NPO may be related to a La Nina-like shift in sea surface temperatures. So, there possibly could be a relationship between La Nina and the EPO, but it's something that needs more investigation.