The ListMinimum response group provides the list IDs for each list returned.
Sample Response (REST)
<?xml version="1.0" encoding="UTF-8"?>
<ListSearchResponse xmlns="http://webservices.amazon.com/AWSECommerceService/2007-01-17">
<OperationRequest>
<HTTPHeaders>
<Header Name="UserAgent" Value="Mozilla/4.0 (compatible; MSIE 6.0; Windows NT 5.1)"/>
</HTTPHeaders>
<RequestId>171Y49VX8YA8R3CKZDXX</RequestId>
<Arguments>
<Argument Name="Service" Value="AWSECommerceService"/>
<Argument Name="AssociateTag" Value="[Your Associate ID Here]"/>
<Argument Name="AWSAccessKeyId" Value="[Your Access Key ID Here]"/>
<Argument Name="ResponseGroup" Value="ListMinimum"/>
<Argument Name="Name" Value="Fred Smith"/>
<Argument Name="ListType" Value="WishList"/>
<Argument Name="Operation" Value="ListSearch"/>
</Arguments>
</OperationRequest>
<Lists>
<Request>
<IsValid>True</IsValid>
</Request>
<TotalResults>76</TotalResults>
<TotalPages>8</TotalPages>
<List>
<ListId>39ZYY4O0UQY2L</ListId>
</List>
<List>
<ListId>3GKIZCP2JMTZT</ListId>
</List>
<List>
<ListId>2CQQERRGX0GHH</ListId>
</List>
<List>
<ListId>E42RKJWERLEX</ListId>
</List>
<List>
<ListId>DRLKV4IEQDWN</ListId>
</List>
<List>
<ListId>1EKKXYDEA3E69</ListId>
</List>
<List>
<ListId>16RL8SF6ARR78</ListId>
</List>
<List>
<ListId>271410NER268W</ListId>
</List>
<List>
<ListId>30G03ZIOWX3IT</ListId>
</List>
<List>
<ListId>1OM7SV07WI1YC</ListId>
</List>
</Lists>
</ListSearchResponse>
The Request that Generated the Response (REST)
http://webservices.amazon.com/onca/xml?Service=AWSECommerceService
&AWSAccessKeyId=[Your Access Key ID Here]
&AssociateTag=[Your Associate ID Here]
&Operation=ListSearch
&ListType=WishList
&Name=Fred%20Smith
&ResponseGroup=ListMinimum