You need 2 things to get this working:

1 - Add an xmlns reference in the root element of your XAML file, to the namespace where your Enum is defined:

<UserControl ...
xmlns:my="clr-namespace:YourEnumNamespace;assembly=YourAssembly">

2 - in the Value property of the DataTrigger, use the {x:Static} form:

<DataTrigger Binding="{Binding Path=LapCounterPingStatus}" Value="{x:Static my:PingStatus.PING_UNKNOWN}">

Notice that the Enum type must be prefixed with the xmlns prefix you defined above.

Edit:

If your Enum is declared inside a class you need to use the syntax:

{x:Static namespace:ClassName+EnumName.EnumValue}

for example:

{x:Static my:ConfigurationViewModel+PingStatus.PING_UNKNOWN}