Final answer:
Diaphragmatic breathing is the best technique to improve lumbar stability in a pilates client. It involves the contraction and relaxation of the diaphragm, engaging deep core muscles for stability.
Step-by-step explanation:
To improve lumbar stability in the pilates client, the best breathing technique to recommend is diaphragmatic breathing. This involves the contraction and relaxation of the diaphragm, which is the main breathing muscle. By focusing on deep breaths where the diaphragm contracts, it helps to engage the deep core muscles, including the transverse abdominis, multifidus, and pelvic floor, which provide stability to the lumbar spine.