Biological process

up regulation of lymphocyte differentiation, up-regulation of lymphocyte differentiation, upregulation of lymphocyte differentiation

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

positive regulation of lymphocyte development

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'.