The first space optical clock (SOC) in the world developed in China, which is composed by five subsystems, including an optical unit, a physics unit, an electronic control unit, a space optical frequency comb, and an ultrastable laser, has been successfully launched with the Mengtian space laboratory into the China Space Station (CSS). Compact and stable lasers are key elements for the operation of the SOC. The optical unit consists of 5 lasers at 461 nm, 679 nm, 689 nm, 707nm, and 813 nm. With a synchronous-tuning-like scheme, high quality external cavity diode lasers (ECDL) have been developed as the seeds. The linewidth of the lasers is suppressed to the order of 100 kHz, and the mode-hop-free tuning range reaches 20 GHz, which meet the requirements of the SOC. With careful mechanical and thermal design, the stability of the lasers against vibration and temperature fluctuation has been sufficiently promoted to confront the challenge of rocket launching. While the power from the ECDL is sufficient for 679 nm and 707 nm repump lasers, additional injection lock is utilized for the 461 nm and 689 nm lasers to amplify the power of the seeds to more than 600 mW, so that efficient first and second stage Doppler cooling can be achieved. To generate an optical lattice with deep enough potential well, over 800 mW 813 nm lasers is required. Therefore, a semiconductor tapered amplifier is adopted to amplify the seed to more than 2 W, so as to cope with various losses of the coupling optics. The wavelength and output power of the 5 lasers are monitored and feedback-controlled by the electronic control unit. All the modules are designed and manufactured as orbital replaceable units, which can be easily replaced by astronauts in case failure occurs. Now the lasers are all turned on and operates normally in CSS. More data of the SOC will be obtained in the near future. At present stage, according to our evaluation, the continuous operation time of the SOC is limited by the injection locked lasers, which are relatively vulnerable to mode hopping. Hopefully this problem can be solved by improving the laser diode manufacturing technology, or developing fiber lasers with compact frequency conversion modules.