Ok, here's my take on it. If your dad and this girl at work had something to hide, they would've been trying to hide it from you. She wouldn't have been eating his lunch with you there. And when you mentioned it to your mom, she knew all about it. If he was messing around with this girl, I bet your mom wouldn't have know who you were talking about, because your dad wouldn't be talking to your mom about sharing lunch with a girl he was having an affair with. When he talked about sharing lunch with everyone, he would leave her out. He would talk about her as little as possible because he would be trying to hide it.
When people work together for a long time, they sometimes become really comfortable with each other, sometimes they become friends. And sometimes they have insides jokes, or a code language, or joke around with phrases like 'luv u much' or 'hug and kisses'. I've done all of that with both guys and girls at work. I had a guy who used to sign a bunch of his emails hugs and kisses. He was being sarcastic most of the time or asking for a favor. It was never anything inappropriate. That is probably the deal with the 'luv u' thing and the '143' thing might be some inside joke or code.
Just info you should be aware of...a lot of companies have very strict policies to protect information and those policies include clauses that if employees share their passwords with anyone (inside or outside the company) thay can be terminated. By accessing your dad's email and telling his co-worker about it, depending on his company's policies, you could have cost him his job.