Lee Merritt tells "TMZ Live" ... Dallas PD obtained a search warrant the day Jean was shot and killed, but not to aid in the investigation -- he believes their goal was to smear and incriminate Botham, even though he did absolutely nothing wrong.

Merritt says the search warrant for Jean's place was specifically to look for drug paraphernalia. He says this shouldn't come as a shock either ... claiming it's just par for the course for American cops.

As for the off-duty cop who killed Jean, Amber Guyger ... Merritt says he's not sure what really went down last Thursday when he shot Jean in his own home -- but he knows she's lying.

If you don't know ... Guyger claims she went to what she thought was her third-floor apartment, but she was actually a floor up at Jean's. She alleges the door was open and she saw a "large silhouette" inside, and claims after her verbal commands were ignored ... she shot Jean in the torso. She says it wasn't until she turned the lights on that she realized she was in the wrong apt.

Witnesses dispute Guyger's story ... saying they heard her knocking and yelling, "Let me in." It's also been pointed out Jean had a distinctive red doormat outside his door, which should have made Guyger realize she was at the wrong place.