want to record lectures and save

Taxlady75 Saud:

"I want the recording saved to my iPhone. Do I need to use Dropbox?"

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Try the Voice Memos app --something typically used by students on college, being they are in classroom lectures. But, I'm not aware of any way of getting a recording in a large auditorium, without echoing coming about. So, Go here: Make a recording in Voice Memos on iPhone - Apple Support

Taxlady75 Said:

"want to record lectures and save: Would like to record lectures and save to phone. Is that possible?"

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Use an External Microphone:

Listen Live seems to be what you are looking for: Use Live Listen with AirPods or Beats - Apple Support