It depends on how much of your case rests on the premises. A prelaunch enterprise can qualify on credible commitments, and equipment need not already be in production use. But if the lease is the principal evidence of committed capital, filing while the tenant name is wrong invites questions you could have answered first.
Sequence the consent request first
Landlord response times are outside your control and vary with the property, so send the consent request early and keep the correspondence. Meanwhile assemble the original funding records and develop the business plan while marking premises-dependent assumptions for revision. Do not treat any waiting period mentioned in planning as a legal requirement. Remember that visa validity and the authorized period of stay after admission are separate, whose end dates may differ.
The interview date depends on consular availability, so the agreements should allow a realistic outside date for closing. E-2 funds must be irrevocably committed and at risk, although properly structured contingencies require fact-specific review; a desired filing date cannot replace that evidence. Once the agreement and escrow are executed and the funds deposited, apply at the consulate; do not book the interview before the money is committed, because the application will be refused for lack of investment.