Add-PSSnapin Microsoft.SharePoint.Powershell -ErrorAction SilentlyContinue
 
#Variables
$WebURL="http://sp2016/sites/dev"
$ParentListName="List3" #Lookup Parent List
$ChildListName="List4" #List to add new lookup value


 
#Get Web and List objects
$Web = Get-SPWeb $WebURL
$ParentList = $Web.Lists.tryGetList($ParentListName)
$ChildList = $Web.Lists.tryGetList($ChildListName)
$query = New-Object Microsoft.SharePoint.SPQuery

 $query.Query = "@
    <Where>
    <And>
    <Eq>
    <FieldRef Name='TESTCOLUME2'/>
    <Value Type='Text'>TEST123</Value>
    </Eq>
    <Eq>
    <FieldRef Name='TESTCOLUME1'/>
    <Value Type='Text'>TEST345</Value>
    </Eq>
    </And>
    </Where>";

$Lookupitem = $ParentList.GetItems($query)

$NewItem=$ChildList.Items.Add()
$NewItem["Title"]="Dec 2014 Milestone"
$NewItem["ColumnName2"] = [string]$Lookupitem.ID + ";#" + $Lookupitem.Title
$NewItem.Update()  
 

write-host "Lookup Field value has been updated!"