High-speed analog-to-digital conversion (ADC) is experimentally demonstrated by employing a time and wavelength interleaved ultra-short optical pulse train to achieve photonic sampling and using wavelength division demultiplexing to realize speed matching between the fast optical front-end and the slow electronic back-end. The sampling optical pulse train is generated from a cavity-less ultra-short optical pulse source involving a packaged device that monolithically integrates an intensity modulator and a phase modulator into a chip based on lithium niobate on insulator (LNOI). In the experiment, the fiber-to-fiber insertion loss of the packaged modulation device is measured to be 6.9 dB. In addition, the half-wave voltages of the Mach-Zehnder modulator and the phase modulator in the LNOI-based modulation device are measured to be 3.6 V and 3.4 V at 5 GHz, respectively. These parameters and the device size are superior to those based on cascaded commercial devices. Through using the packaged modulation device, two ultra-short optical pulse trains centered at 1541.40 nm and 1555.64 nm are generated with time jitters of 19.2 fs and 18.9 fs in the integral offset frequency range of 1 kHz to 10 MHz, respectively, and are perfectly time interleaved into a single pulse train with a repetition rate of 10 GHz and a time jitter of 19.8 fs. Based on the time and wavelength interleaved ultra-short optical pulse train, direct digitization of microwave signals within the frequency range of 1 GHz to 40 GHz is demonstrated by using a two-channel wavelength demultiplexing photonic ADC architecture, where the effective number of bits are 5.85 bits and 3.75 bits for the input signal at 1.1 GHz and 36.3 GHz, respectively.