Well if she comes into any of the diseases she would have been immunised for then theres a chance she can pick them up.
Clink will need COD from ur doctor stating u've spoken to them and have decided to delay lulu's vaccinations.
it all depends on how long u want to delay them for, if u want to give them to her at all, if its only a few months then u dnt need to worry about clink.

My advice would be to look up the diseases the immunisations cover and see the if that something u willing to risk lulu getting. (bearing in mind that immunisations arent 100% anyway and theres still a chance she might get diseases she's been vacced for anyway)