Why and how does lycopene absorbance increase with heating?
"Heating will result in an increase in amount of lycopene absorbed by
  the body."
  Is the statement scientifically correct?


It is a poorly phrased statement, but it is probably generally true.  It would have been better to say something like, "heating tomatoes will increase the amount of all-trans-lycopene available for ingestion."

Here's a link to a full paper on the subject (click the "View" button near the top-right of the page).  Basically two things are going on at the same time when lycopene containg food is heated.  It is the naturally occurring, all-trans isomer of lycopene that is thought to be beneficial to the human body. Heating lycopene causes it to isomerize to a variety of cis-isomers.  Heating in the presence of oxygen can also cause oxidation.  Both of these processes (isomerization and oxidation) reduce the potency of the lycopene in the broth.  

However, in parallel with these deleterious effects, heating also makes more lycopene available in the heated broth or extract.  This is because heating disrupts cell walls and releases lycopene from the cells.  The above link shows that, at least at moderate temperatures, the latter effect predominates and so more active all-trans-lycopene is made available upon heating tomatoes, despite the loss of some lycopene to isomerization and oxidation.