Long travel day!
Baggage will be checked through. The morning LHR flight will depart from the same terminal the HNL flight arrives from, C. As HNL-EWR is domestic, you will be able to walk from one gate to another and will do the document check at the LHR gate. You will likely need to switch C concourses though, won't be longer than a 10-15 minute walk between gates max.