Ironically I'd never heard of the ILAC method before. I don't recall ever being taught that when I studied law, or if I did I have since forgotten it. Seems to be a fine way of structuring your answer either way.
I don't know to what extent you have studied contract law and tort law, but you need to start by separating them out. Address each of them individually and go through each of the main issues that generally falls within those areas. So for example, something like this:
CONTRACT: There is clearly a valid contract between the parties. On the face of it Lovely Lighting Ltd have breached the contract because they have not provided a sign in line with what Bart ordered. There are four basic areas that Bart would want to be compensated for;
i) A new sign because the old one was wrong;
ii) In the alternative, a new sign because the old one was faulty and was destroyed when it caught fire;
iii) Damages for the painting that was destroyed in the fire;
iv) Damages for personal injury caused to Bart
So you need to consider whether the law of contract generally would allow Bart to be compensated for those particular areas. If you conclude that Bart would ordinarily be able to recover damages in some or all of those areas, you then need to consider whether the terms of the contract that exonerate Lovely Lighting of liability are valid and offer the protection that they seem to provide on the face of it. The fact that Bart didn't read the written agreement is also something that may be relevant.
PERSONAL INJURY: Same process, as the areas of compensation are the same, but this time it's in tort law. So, does tort law allow Bart to recover damages in principle in those areas? If so, is there are a causative link between the negligence and the individual heads of loss? Is the damage foreseeable? Is it too remote? If you think there could be liability to some extent, does the exclusion clause have effect? In other words, can you use a term of a contract to exclude liability for personal injury and/or other damages arising out of a tortious breach?
It may well be that I've missed something, as that's off the top of my head having scanned over the question, but hopefully that's given you some degree of assistance.