Can a house appraser tell you that you have to get a lead paint inspection?

It can vary by state, but generally, yes.

If the appaiser is inspecting the house because you are aquiring a federal fund loan, such as 203 (k), or first -time home buyer, then the requirement is that the paint must be intact on a pre-1978 house. If it is not, it can be presumed to be lead paint or it can be tested by a lead inspector and shown to be negative, therefore not requiring use of lead abatement or EPA RRP contractors to fix the deteriorated paint.