I think Liefong led Meehan down the rosey red path and told him no worries about leaving out the hugely exculpatory fact that several other, separate men's DNA was found in or on her.
Meehan is probably a sadder but wiser man now, but I think his greed to get more business brought him to this point. At the very best, he looks like a third-rate amateur in his industry.
There must have been any number of labs Liefong could have chosen. Why this one? Did he do some personal and financial research on Meehan and his lab and figured he could roll Meehan pretty easily?
"Only The Shadow Knows."