In broad terms lowest common denominator (by production standards) means a subject of interest or contemporary values for which the target audience most likely shares, understands and identify with. Incorporating such a standard into production can turn a simple story into an "entertaining" vehicle. It can make the most boring subject compelling, sexy, fascinating, riveting, ect. for the target audience. In other words, make the plot and emotional trials and tribulations ordinary or common enough for your target audience and you can make dirt sympathetic. Throw in some contemporary dialog and popular belief systems and you can turn that dirt into a hot iconic hero.
And therein lies the inherent problem. It is too easy (and often too tempting) to use the LCD to compel one's audience to think a certain way. This is most notably easy to do with commercial endeavors aimed at children and youths. This is why I used "Dickinson" as reference. Don't get me wrong - I have loved Emily Dickinson's poetry since I was a teen- but the description of this series makes it pretty clear they are using her as a vehicle to "address" modern social issues. And when I think of the valuable insight kids could learn by an honest presentation of the woman and her life as opposed to this fluff, it rather sickens me.
