Using SQLCMD with Variables
You could try a "script the script" approach by using the SQLCMD :out command to redirect output, with :connect and optionally :r to read the output, something like this:

SET NOCOUNT ON

DECLARE @tbl TABLE (Id int IDENTITY (1, 1),ServerName sysname, DbName sysname, IsDone BIT DEFAULT(0))

INSERT INTO @tbl (ServerName,DbName) VALUES (N'CZASQL-001', N'[Lps_FinishPack_CZ]')
INSERT INTO @tbl (ServerName,DbName) VALUES (N'LS_LPS_DK',  N'[Lps_FinishPack_DK]')
INSERT INTO @tbl (ServerName,DbName) VALUES (N'LS_LPS_DK',  N'[Lps_FinishPack_NY]')
INSERT INTO @tbl (ServerName,DbName) VALUES (N'LS_LPS_DK',  N'[Lps_FinishPack_Supplier]')
INSERT INTO @tbl (ServerName,DbName) VALUES (N'LS_LPS_372', N'[Lps_FinishPack_MO]')
INSERT INTO @tbl (ServerName,DbName) VALUES (N'LS_LPS_678', N'[Lps_FinishPack_678]')

:out d:\temp\temp.sql

SELECT 
    ':connect ' + serverName + '
USE ' + dbName + '
SELECT * FROM [config].[LpsPlant]
GO
'
FROM @tbl
GO

:out STDOUT
GO

-- Optionally read/run the output
--:r d:\temp\temp.sql


Run the script then go and have a look in the temp.sql file. Mine looks like this:



If you are happy with the output, uncomment the :r to run it, or just run/edit the script you have created.

Hope that makes sense.