AliCPT-1 is the first Chinese CMB experiment aiming for high precision measurement of Cosmic Microwave Background B-mode polarization. The telescope, currently under deployment in Tibet, will observe in two frequency bands centered at 90 and 150 GHz. We forecast the CMB lensing reconstruction, lensing-galaxy as well as lensing-CIB (Cosmic Infrared Background) cross correlation signal-to-noise ratio (SNR) for AliCPT-1. We consider two stages with different integrated observation time, namely "4 module*yr" (first stage) and "48 module*yr" (final stage). For lensing reconstruction, we use three different quadratic estimators, namely temperature-only, polarization-only and minimum-variance estimators, using curved sky geometry. We take into account the impact of inhomogeneous hit counts as well as of the mean-field bias due to incomplete sky coverage. In the first stage, our results show that the 150 GHz channel is able to measure the lensing signal at 15Ο significance with the minimum-variance estimator. In the final stage, the measurement significance will increase to 31Ο. We also combine the two frequency data in the harmonic domain to optimize the SNR. Our result show that the coadding procedure can significantly reduce the reconstruction bias in the multiple range > 800. Thanks to the high quality of the polarization data in the final stage of AliCPT-1, the EB estimator will dominate the lensing reconstruction in this stage. We also estimate the SNR of cross-correlations between AliCPT-1 CMB lensing and other tracers of the large scale structure of the universe. For its cross-correlation with DESI galaxies/quasars, we report the cross-correlation SNR = 10 βΌ 20 for the 4 redshift bins at 0.05 < z < 2.1. In the first stage, the total SNR is about 32. In the final stage, the lensing-galaxy cross-correlation can reach SNR=52. For lensing-CIB cross-correlation, in the first stage, the cross-correlation between AliCPT-1 lensing and Planck CIB 353, 545, 857 GHz channels are about SNR=18, 19, 23 respectively. In the final stage, the cross-correlation can reach SNR=25, 33 and 42. Due to the strong correlations between frequency bands, the total lensing-CIB cross-correlation by combining the three frequencies in Planck CIBs are SNR=23 and 43 for the AliCPT-1 first and final stage, respectively.