We're still short information here: now you're telling us you have two PNRs, but we still don't know what those entail; that could make a significant difference. "The devil's in the details" applies here.

If these are separately ticketed - the EI and VS - you'll certainly not have trouble dropping the EI sector between London and Dublin and checking baggage to LHR.

If so, do check what could (or could not occur) if your EI flight into LHR is delayed; will VS honor your ticket if you miss your flight to LAX?

Safe travels!