Praise be to Allah.
We appreciate your keenness to convey the message of Islam to people, and your keenness to implement the Sunnah and not go against sharee‘ah. We ask Allah, may He be exalted, to make things easy for you and to grant you the best of rewards.
Praying in congregation in the mosque is obligatory for everyone who can hear the call to prayer in an ordinary voice without any barriers and without amplification through loudspeakers. The more correct scholarly view is that it is only obligatory in a mosque in which the call for prayer is given.
For more information see the answer to question no. 38881
But there may be some cases in which shar‘i needs or important interests make it permissible for a group of Muslims to offer prayer in congregation somewhere other than in the mosque.
There is no doubt that calling non-Muslims to Islam is an important aim. If you think it most likely that your praying in the lecture hall will have an impact on them, and may be the cause of some of them becoming Muslim, then there is nothing wrong with praying in the lecture hall. So you can give the adhaan and iqaamah, and pray in congregation.
If that is done every year, it is not bid‘ah (an innovation), because the aim behind it is a legitimate shar‘i aim, namely openly practising the rituals of Islam and calling non-Muslims to the faith. But you should not set a specific date for that every year or every month and so on; rather that should be done according to need. Then you can do it on different days and choose the best day to get the largest congregation and so that the largest possible number of non-Muslims can watch.
And Allah knows best.