We study six luminous Lyα emitters (LAEs) with very blue rest-frame UV continua at 5.7 ≤ z ≤ 6.6. These LAEs have previous Hubble Space Telescope (HST) and Spitzer IRAC observations. Combining our newly acquired HST images, we find that their UV-continuum slopes β are in a range of -3.4 ≤ β ≤ -2.6. Unlike previous, tentative detections of β ≃ -3 in photometrically selected, low-luminosity galaxies, our LAEs are spectroscopically confirmed and luminous (MUV < -20 mag). We model their broadband spectral energy distributions (SEDs), and find that two β ≃ -2.6 ± 0.2 galaxies can be well fitted with young and dust-free stellar populations. However, it becomes increasingly difficult to fit bluer galaxies. We explore further interpretations by including the non-zero LyC escape fraction fesc, very low metallicities, and/or active galactic nucleus contributions. Assuming fesc ≃ 0.2, we achieve the bluest slopes β ≃ -2.7 when nebular emission is considered. This can nearly explain the SEDs of two galaxies with β ≃ -2.8 and -2.9 (σβ = 0.15). Larger fesc values and very low metallicities are not favored by the strong nebular line emission (evidenced by the IRAC flux) or the observed (IRAC 1 - IRAC 2) color. Finally, we find that the β ≃ -2.9 galaxy can potentially be well explained by the combination of a very young population with a high fesc (≥0.5) and an old, dusty population. We are not able to produce two β ≃ -3.4 ± 0.4 galaxies. Future deep spectroscopic observations are needed to fully understand these galaxies.