What is your reaction when he starts to act like that in public? Do you baby him and comfort him or do you just ignore it?

After dealing with a couple of dogs who freaked out in public and having one now that most likely will have sort of the same problem (that would Beaker, he wasn't properly socialized and as a result he doesn't quite know what to think of some things) I have found that the best thing to do in situations like that is to put it bluntly make the dog deal with it.

If you start acknowledging the dogs behaviour they're more likely to continue to do it while if you ignore it and don't really give them a choice they eventually figure out that if mom is okay with it then I should be fine as well. So far that thinking has been doing wonders for Beaker as a lot of stuff that I think he would totally loose his mind to he's been doing quite well with because I've kept calm and just made him face it.

Just take baby steps, go some place near your house for a few minutes and if Lucky starts to freak ignore it (I know it will be hard to do, truse me I know. I still have a hard time if Winter freaks) but if he kind of settles down a little even if it's for a second or two heap tons of praise and attention on him so he knows that it's not a bad thing. Then keep doing stuff like that until he can handle the situation for longer periods and eventually he might get to a point where he'll take a treat or something along those lines. Just remember to stay calm and don't get stressed by it.

As for the agility if you could find a good place to take classes with a good instructor you might be able to explain your situtation to them and see if it's something that they would be willing to work with in class or perhaps give you some homework to work on, for it. I know the classes that I help at we have all types of dogs with different problems and my friend is always willing to give them advice and stuff to work on at home to help them get over any problems they might be having.

I know that when I started agility Smudge was not really in a postition to always handle the class but we took our time and worked slowly with him and now we're advancing through the levels and have made it into the high stress situtation that is Superdogs.