Dear Dorsa Sattari many thanks for your interesting technical question. Unfortunately I cannot give a competent personal advice as we work in a completely different discipline (organometallic chemistry). However, it is often quite helpful to search RG for possible answers. In this context please have a look at the following overview on Questions related to Competent Cell Preparation. Perhaps some of the answers to these questions are helpful for you:

https://www.researchgate.net/topic/Competent-Cell-Preparation

What does the manufacturer say about growth - only leucine auxotrophy? To make sure it is actually viable, have you tried growing it in complex medium like Luria?

E. coli Auxotrophs for Amino Acid-Selective Isotope Labeling: The approach is to produce proteins in E. coli auxotrophic strains in which enzymes that result in dilution and scrambling of the label have been eliminated, avoiding mutations or groups of mutations that would result in impeding cell growth. https://www.sciencedirect.com/science/article/pii/S0076687915003109

Check https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3400592/