Dear {Lecturer Name}
Please accept my sincerest apology for not providing the suitable {environment, tools, equipment etc…} you{requested/needed} for your lecture at {event/location} on {M/DD/YYYY}.
What happened during your lecture at {event/location} was inappropriate and was extremely unprofessional on our part. I understand the situation prevented you from giving the lecture you had prepared. We have taken steps to make sure this won’t happen again, and I hope that it will not stop you from coming back in the future.
We value your insights and recognize your {accomplishments, dedication, expert knowledge, etc…} in {field, educating, community service, etc…} and promise that we will be fully prepared should you decide to visit us again.
Sincerely,
{Your Name}
{Your Name}