Is it permissible to work as a lecturer in a mixed-gender university, knowing that the percentage of female students is dominant, and that the need for this work is spiritual/moral, not financial?

A woman's work is permissible and lawful if it does not involve religious transgressions or temptation (fitna). It may even be recommended if there is a need for it among Muslims. The basic principle is that it should not involve mixing with foreign men. However, if temptation is safeguarded against, and there is no private seclusion (khalwa (definition)) or suspicious mixing, then there is no harm in the aforementioned work, especially if the intention is good and there is a desire to call people to Allah and benefit the Ummah.