Note that immunologists typically use the word 'development' to refer to cells of B or T cell lineages undergoing the process that GO describes as 'cell differentiation'.

Any process that activates or increases the frequency, rate or extent of lymphocyte differentiation.

upregulation of lymphocyte differentiation

up regulation of lymphocyte differentiation

up-regulation of lymphocyte differentiation

stimulation of lymphocyte differentiation

activation of lymphocyte differentiation

biological_process

positive regulation of lymphocyte development

GO:0045621