True. And you're likely to lose your team's trust to. If employees see a leader telling white lies to potential customers (or to anyone) they're likely to ask "I wonder what white lies they're telling me?"
Those are the real morale killers - knowing that you might need to start stressing and crunching at any moment, and that the roadmaps you have aren't real. Nor are your commitments to anyone working in the company if you get pulled off your planned work to service a white lie. They just complicate everything.
An executive lying to customers is a huge liability. I won't take an ethical stance on it, but in a business sense, the lies incur a debt that must be paid.