$siteField = Get-PnPField -Identity ThisField
if ($siteField) {
    [xml]$schemaXml = $siteField.SchemaXml
    $schemaXml.Field.ShowField = "NewShowField"
    Set-PnPField -Identity ThisField-Values @{SchemaXml=$schemaXml.OuterXml}
}

$dlin = New-Object System.Collections.Generic.List[String]
$dlin.Add("OtherField1")
$dlin.Add("OtherField2")
$values = @{LookupField = "NewShowField"; DepentantLookupInternalNames = $dlin}