The world's first space optical clock (SOC) developed in China, which is composed of five subsystems, i.e. an optical unit, a physics unit, an electronic control unit, a space optical frequency comb, and an ultrastable laser, was successfully launched with the Mengtian space laboratory on October 31, 2022, and entered into the China Space Station (CSS). Compact and stable laser is a key element for the operation of the SOC. The optical unit consists of 5 lasers with wavelengths of 461, 679, 689, 707 and 813 nm, respectively. With a synchronous-tuning-like scheme, high-quality external cavity diode lasers (ECDLs) are developed as the seeds. The linewidths of the lasers are all reduced to approximately 100 kHz, and their tuning ranges, free from mode hopping, are capable of reaching 20 GHz, satisfying the requirements for the SOC. With careful mechanical and thermal design, the stability of the laser against vibration and temperature fluctuation is sufficiently promoted to confront the challenge of rocket launching. While the power from the ECDL is sufficient for 679-nm repump laser and 707-nm repump laser, additional injection lock is utilized for the 461-nm laser and 689-nm laser to amplify the power of the seeds to more than 600 mW, so that effective 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 are 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 wavelengths and output power values of the 5 lasers are monitored and feedback is controlled by the electronic control unit. All the modules are designed and prepared as orbital replaceable units, which can be easily replaced by astronauts in case failure occurs. Now the lasers are all turned on and operate 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 preparing technology, or developing fiber lasers with compact frequency conversion modules.