As for deeply buried and heterogeneous carbonate reservoirs, which require long well-drilling periods with high cost, we carried a pilot test for lateral horizontal well with 4th-level well completion in Kazakhstan K oilfield in order to increase the well-controlled area and production rate of horizontal wells. Meanwhile, the process also aimed to enhance the degree of formation development and take full advantage of the idea of "fewer wells and higher production". Firstly, according to in-room laboratory test results, a clean self-diverting acid system was determined. The performance of the self-diverting acid in temporary blocking, retarding and low damage was tested. In practice, well trajectories of the two laterals were drilled in the pattern of three sections: vertical, angle increasing, and deviated. After the completion of the well, the secondary lateral was acidized by the diverting acid mixed with nitrogen, and the primary lateral was treated by drawing back coiled tubing. Subsequently, the two laterals went into operation at the same time. We optimize the treating pressure, the pumping rate, and coiled tubing drawing back velocity based on the formation, rock properties and physical properties of this oilfield. We calculate the skin factor after acidization. Results indicate that both of these two branches are acidized successfully thus restoring the productivity significantly, which implies broad application prospects of the lateral horizontal well drilling with acidizing technology in the oilfield.