If you are hooked Blu-Ray HDMI directly to the TV and getting the audio from the TV you should not have a lip sync issue. As suggested you should ensure you have current firmware on your DVD player. (this is another wonderful "advancement" or feature that comes with Blu-Ray, having to update the firmware from time to time, I only do mine when a Disc will not play, but I have heard others say they have solved other issues with the upgrades) I am from the "if ain't broke don't fix it school"...
The quality of the HDMI cable is unlikely to be a part of the issue but you never know, were they three cables of all roughly the same price and brand? (Not that I am a Monster fan at all, but you might find a store where you can get your money back and a get a high end Monster cable that you can return if it makes not difference.)
In your DVD setting there should be a sound/lip sync control while this is usually for delays caused running though various parts of a Home Theater system and the TV, it could be in your TV if it is doing anything in the audio path.
Check your DVD settings menu for this setting, no matter what it is called it should be clear that it is to sync the picture and sound, everyone seems to call it something different, can be Delay, Audio Sync, Lip Sync, etc...
Mess with control, mine has a center 0 setting and then you can delay the sound going minus or advance the sound going plus, thankfully I have no needed it, the picture and sound between my panni TV is in sync no matter how I source route it, through the HT receiver or direct TV so I have neve had to mess with the control.
If you end up switching DVD players again consider the Panosonic DMP-BD80K, I just upgraded from DMP-35 and both are great and no lip sync issues.
Now for your DVD performance, you need to be more specific, if it is picture quality then there can ba a slew of differnt answers, if it is that it take for what seems like forever to load, to transition menu's, for dialogs to open, like settings, then welcome to Blu-Ray, compared to a regular DVD player at least at this time it is the price you have to pay for Blu-Ray, a system that is slower than molassas in the winter, again, compared to a SD DVD player.
My new is a lot faster than on old one, but still, I can almost make pop-corn in the time it does something and if it gets confused and they do, the best answer I have found, is turn it off, and back on again and start over, once it gets confused it stays confused, I guess this is what Java has bought us in our living room.