Context. Lyman alpha (Lyα) emitting galaxies (LAEs) are used to probe the distant universe and are therefore important for galaxy evolution studies and for providing clues to the nature of the epoch of reionization. However, the exact circumstances under which Lyα escapes a galaxy are still not fully understood. Aims. The Trident project is designed to simultaneously examine Lyα, Hα, and Lyman continuum emission from galaxies at redshift z ∼ 2, thus linking these three aspects of ionizing radiation in galaxies. In this paper, we outline the strategy of this project and examine the properties of LAEs in the GOODS North field. Methods. We performed a narrowband LAE survey in GOODS North using existing filters and two custom made filters at the Nordic Optical Telescope with MOSCA. We use complementary broadband archival data in the field to make a careful candidate selection and perform optical to near-IR SED fitting. We also estimate far-IR luminosities by matching our candidates to detections in Spitzer/MIPS 24 μm and Herschel/PACS catalogues. Results. We find a total of 25 LAE candidates, probing mainly the bright end of the LAE luminosity function with L Lyα ∼ 1−15 × 10 42 erg s −1 . They display a range of masses of ∼0.5−50 × 10 9 M , and average ages from a few tens of Myr to 1 Gyr when assuming a constant star formation history. The majority of our candidates also show signs of recent elevated star formation. Three candidates have counterparts in the GOODS-Herschel far-IR catalogue, with luminosities consistent with ultra-luminous infrared galaxies (ULIRGs). Conclusions. The wide range of parameters derived from our SED fitting, as well as part of our sample being detected as ULIRGs, seems to indicate that at these Lyα luminosities, LAEs do not necessarily have to be young dwarfs, and that a lack of dust is not required for Lyα to escape.