I would NOT recommend a lookup select box.
1st- it won't solve your problem, you can only single-select in a Lookup Select Box.
2nd- lookup select boxes are notorious for hogging system resources, you will notice that your lookup select box on a form will take unnecessarily long to load and it will create a terrible user experience. Even ServiceNow themselves recommends against using this due to this reason. Not sure why it hasn't been fixed yet, but it's probably because not enough people have complained about it (as we've seen that's usually the only way to get something like this fixed)
3rd- Related to #2, you are just better off created a Select box with it's own question choices so it loads properly in the portal.
4th- I've found the 2 best ways to do a "multi-select" on the portal is to use a list collector, or, to create a series of checkboxes next to each other with a Label in front of it. When consecutive checkboxes are visible on the form, the system will essentially "bundle" these checkboxes together so if 1 checkbox is checked, it satisfies the mandatory value for all the checkboxes. This method will allow you to have a label with multiple checkboxes under it, you will have the red asterisk indicating a selection is mandatory, and the mandatory value will be satisfied if 1 or more checkboxes is checked.
Hope this helps.
DJR
