We searched for z= 7.3 Lyα emitters (LAEs) behind two gravitationally lensing clusters, Abell 2390 and CL 0024, using the Subaru Telescope Suprime-Cam and a narrow-band filter NB1006 (λc˜ 1005 nm and full width at half-maximum of about 21 nm). The combination of the fully depleted CCDs of the Suprime-Cam, sensitive to z˜ 7 Lyα emission at ˜ 1 μm, and the magnification by the lensing clusters can be potentially a powerful tool to detect faint distant LAEs. Using the NB1006 and deep optical to mid-infrared images of the clusters taken with the Hubble Space Telescope and Spitzer Space Telescope, we investigated if there exist objects consistent with the colour of z= 7.3 LAEs behind the clusters. We could not detect any LAEs to the unlensed Lyα line flux limit of FLyα≃ 6.9 × 10-18 erg s-1 cm-2. Using several z=7 Lyα luminosity functions (LFs) from the literature, we estimated and compared the expected detection numbers of z˜ 7$ LAEs in lensing and blank field surveys in the case of using an 8-m class ground-based telescope. Given the steep bright-end slope of the LFs, when the detector field of view (FOV) is comparable to the angular extent of a massive lensing cluster, imaging cluster(s) is (are) more efficient in detecting z˜ 7 LAEs than imaging a blank field. However, the gain is expected to be modest, a factor of 2 at most and likely much less depending on the adopted LFs. The main advantage of lensing survey, therefore, remains the gain in depth and not necessarily in detection efficiency. For much larger detectors, the lensing effect becomes negligible and the efficiency of LAE detection is proportional to the instrumental FOV. We also investigated the NB1006 images of the three z˜ 7 z-dropout galaxy candidates previously detected in Abell 2390 and found that none of them is detected in NB1006. Two of them are consistent with the predictions from previous studies that they would be at lower redshifts. The other one has a photometric redshift of z≃ 7.3, and if we assume that it is at z= 7.3, the unlensed Lyα line flux would be very faint: FLyα < 4.4 × 10-18 erg s-1 cm-2 (1σ upper limit) or equivalent width of ? Å. Its Lyα emission might be attenuated by neutral hydrogen, as recent studies show that the fraction of Lyman break galaxies displaying strong Lyα emission is lower at z˜ 7 than at z≲ 6.