The Ly alpha escape fraction is a key measure to constrain the neutral state of the intergalactic medium and then to understand how the universe was fully reionized. We combine deep narrowband imaging data from the custom-made filter NB393 and the H2S1 filter centered at 2.14 mu m to examine the Ly alpha emitters and H alpha emitters at the same redshift z - 2.24. The combination of these two populations allows us to determine the Ly alpha escape fraction at z = 2.24. Over an area of 383 arcmin(2) in the Extended Chandra Deep Field South (ECDFS), 124 Ly alpha emitters are detected down to NB393 = 26.4 mag at the 5 sigma level, and 56 H alpha emitters come from An et al. Of these, four have both Ly alpha and H alpha emissions (LAHAEs). We also collect the Ly alpha emitters and H alpha emitters at z = 2.24 in the COSMOS field from the literature, and increase the number of LAHAEs to 15 in total. About one-third of them are AGNs. We measure the individual/volumetric Ly alpha escape fraction by comparing the observed Ly alpha luminosity/luminosity density to the extinction-corrected Ha luminosity/luminosity density. We revisit the extinction correction for H alpha emitters using the Galactic extinction law with color excess for nebular emission. We also adopt the Calzetti extinction law together with an identical color excess for stellar and nebular regions to explore how the uncertainties in extinction correction affect the estimate of individual and global Ly alpha escape fractions. In both cases, an anti-correlation between the Ly alpha escape fraction and dust attenuation is found among the LAHAEs, suggesting that dust absorption is responsible for the suppression of the escaping Ly alpha photons. However, the estimated Ly alpha escape fraction of individual LAHAEs varies by up to similar to 3 percentage points between the two methods of extinction correction. We find the global Ly alpha escape fraction at z = 2.24 to be ( 3.7 +/- 1.4)% in the ECDFS. The variation in the color excess of the extinction causes a discrepancy of similar to 1 percentage point in the global Ly alpha escape fraction.