Is there a number visible on the top of that smd component? I can't see in the picture, like you said, where it's burnt.
The iron like N6BY suggested and the one Ke4est posted a link to will work if you have decent eyesight and a steady hand. I wouldn't really recommend trying it with your Weller gun. For single smd component work, I'll usually just use my Hako station that's like the one Ke4est posted because I sold all my smd stations when I closed my repair shops years ago and went into the electronics recycling.
The small stuff like smd devices have been real hard for me the past few years though, my eyes have gotten really bad these past few years. Very frustrating, fresh out of trade school I worked repairing hearing aids under a microscope, then for years afterward worked in my own repair shops. Now I restore cars and my darn eyes are getting too bad for that even.
Lightning's a funny beast. When I owned my repair shops, I loved thunder storms rolling through our area, so much work would come in from them. Most stuff would be fixable, but sometimes it would just totally trash stuff or hit really odd areas and components. Back then though, stuff was a bit tougher than now.
On your V-Box, the chip that's burnt, you could try pulling it out of circuit and put the regulators back in circuit, see if your regulator voltages are normal then. But then I think Ke4est mentioned you'd have the problem of flashing a new chip, I think? But there may be a way for that. Course, it might be more than just that too. I plan on popping the cover off of one of my V Boxes soon so I can know the circuit better, never had to work on one of them yet. Check out that chip too, while I'm in there.
Too bad it wasn't just the trace in the LNB, that would've been nice and easy!