Aggressive double- and triple-hit (DH/TH) diffuse large B-cell lymphomas (DLBCLs) feature activation of Hsp90 stress pathways. Herein, we show that Hsp90 controls posttranscriptional dynamics of key messenger RNA (mRNA) species including those encoding BCL6, MYC, and BCL2. Using a proteomics approach, we found that Hsp90 binds to and maintains activity of eIF4E. eIF4E drives nuclear export and translation of BCL6, MYC, and BCL2 mRNA. eIF4E RNA-immunoprecipitation sequencing in DLBCL suggests that nuclear eIF4E controls an extended program that includes B-cell receptor signaling, cellular metabolism, and epigenetic regulation. Accordingly, eIF4E was required for survival of DLBCL including the most aggressive subtypes, DH/TH lymphomas. Indeed, eIF4E inhibition induces tumor regression in cell line and patient-derived tumorgrafts of TH-DLBCL, even in the presence of elevated Hsp90 activity. Targeting Hsp90 is typically limited by counterregulatory elevation of Hsp70B, which induces resistance to Hsp90 inhibitors. Surprisingly, we identify Hsp70 mRNA as an eIF4E target. In this way, eIF4E inhibition can overcome drug resistance to Hsp90 inhibitors. Accordingly, rational combinatorial inhibition of eIF4E and Hsp90 inhibitors resulted in cooperative antilymphoma activity in DH/TH DLBCL in vitro and in vivo.