Regardless of you getting distracted or little white lies you may have told him, I'd call this behavior a definite warning sign. You don't "deserve" to not be trusted, and if he's starting to make stuff up (i.e. "you're talking to someone else") and getting aggressive, that sounds like he's only going to get more distrustful and controlling. Please consider this, and if he starts doing things like going through your phone, threatening you or restricting who you talk to, I'd suggest you get out as fast as you can.
I may have lied to him but that's a few times, sometimes we must lie..
it might help us to help you if you give an example of when you {must) lie..
it would help if you told us if he has caught you in a lie, and what it was about
(how many lies, and when did they happen).
it's hard to get the right advice if we don't know the details, as the saying goes "the devil is in the details".
As for your not being fully there, and totally engaged when talking to him o the phone, i suggest you do shut the lid of the computer or turn off the volume of the tv and take his call, or he'll soon be making it to a girl who he figures values him, more than you do.
Sounds like you should stop lying about things and stop browsing the internet while you talk on the phone. Both things are rude and disrespectful. And of course he's going to think you are a liar when he catches you in a lie. Do you honestly expect him to trust you?
Back before we had computers in our houses, we used to actually listen to people when they were talking to us on the phone. Because you know, they're taking time out of their day to talk to you. It's pretty rude to be distracted while talking on the phone. You should shut off the computer and listen and be engaged in the conversation because that's the proper thing to do.
Even if you are not lying to him, you are saying he is not as important to you as your computer. I'd say most boyfriends would find that rather offensive.