If your pair of lines will only appear once in your file, you could use
File.ReadLines(pathToTextFile)
.SkipWhile(line => !line.Contains("CustomerEN"))
.Skip(1) // optional
.TakeWhile(line => !line.Contains("CustomerCh"));
If you could have multiple occurrences in one file, you're probably better off using a regular foreach loop - reading lines, keeping track of whether you're currently inside or outside a customer etc:
List<List<string>> groups = new List<List<string>>();
List<string> current = null;
foreach (var line in File.ReadAllLines(pathToFile))
{
if (line.Contains("CustomerEN") && current == null)
current = new List<string>();
else if (line.Contains("CustomerCh") && current != null)
{
groups.Add(current);
current = null;
}
if (current != null)
current.Add(line);
}