King Lear - Do you think the main plot and sub plot run parallel in King Lear. Discuss?

Deception and lies are what makes King Lear a tragedy. The play is a result, of the consequences triggered off by lies and falsehoods that were told in King Lea's family, as well as in the family of the Earl of Gloucester. In this play, Shakespeare added a sub-plot to the main-plot and both are based on the same events, differing slightly according to the story.
The main-plot involves Lear and his three daughters whereas the sub-plot makes use of Gloucester and his two sons. King Lear gives his daughters a love-test, stupidly intending to measure love with flattery; "Which of you shall…