Just to argue...
...No actually to help....honestly!
The difference between curd and the "cream" the real name for what I called butter is the amount of butter. (Traditional lemon curd didn't have butter that is a modern and often regional addition and it isn't required for lemon curd.) and actually process of making can alter the structure of a food making it safer or easier to use. So actually it is not a "curd" at all.
Yeah I like to bicker. Anyway you need to decide your own comfort level of what to leave at room temperature. Also depending on what "outside" means . Are we talking Florida in August? and for how long. If you are assembling for same day service there is not problem. If you are doing it in advance - is there room in the freezer, then just pull it out the morning of and let thaw, that will keep it cool.
Don't tell the health dept. but sugar and lemon juice go a long way towards keeping egg based products safe, for a short time. The ratio of eggs is not that high, also the higher the fat content the more time you can buy as well. Most cakes might be stored in fridge to keep longer in bakeries but are designed to be eaten at room temp. Most traditional buttercreams are designed this way. Also you don't refridgerate a lemon merengue pie after it is made.
If you make good lemon curd just go for it. Make sure it cooks above 180 degrees. I am sure their fridge will let them hold a container of curd until it is all the way chilled, then make the cake. Or use a big ice-chest. I guess I just hate to see people compromise on quality ingredients. There are lots of creative storage solutions.