"Influence of media in our lives," or "influence of media on our lives?"

Both in and on are correct and used in this case. There is no absolute rule but it seems that for some people there may be a slight distinction between "influence of media on people" and "influence of media in things" which would incline me toward "influence of media in our lives".

You can change the grammar to remove the proposition, for example "how media influences our lives", providing that you are happy using a singular verb with a Latin plural noun.

They're both correct, with a slight distinction in meaning.

• If you speak of the influence of media in our lives, then I feel there's an implication that the media is just one of several things influencing us.

• If you speak of the influence of media on our lives, then I expect the media to be the only influence under discussion.

I don't know whether this distinction is specific to "the media", so let me posit some new phrases:

• The influence of religion in modern life
• The influence of religion on modern life

Yup, the distinction's still there: to me, "in" implies one of many influences, while "on" implies a more all-encompassing influence.

When I read the two sentences I distinguish the meanings of the two as such:

(Influence of) (media in our lives)

(Influence of media) (on our lives)

A rewording to make it more clear:

This is the influence that the media in our lives has on [something].

This is the influence that the media has on our lives.

This is not a necessary distinction, however, and you can legitimately say:

This is the influence that the media has in our lives.

There is another difference between using "in" and "on" in this context. "In" implies that something is happening within our lives or that something is affecting our lives from the inside. "On" implies a more distant, abstract influence: Something is happen to our lives from the outside or to our lives as a whole.

I worked in that building.

I worked on that building.