I know we can easily do this by a simple loop, but I want to persue this LINQ/Predicate?
string[] columnNames = dt.Columns.?
or
string[] columnNames = from DataColumn dc in dt.Columns select dc.name;
Try this (LINQ method syntax):
string[] columnNames = dt.Columns.Cast<DataColumn>()
                                 .Select(x => x.ColumnName)
                                 .ToArray();  
or in LINQ Query syntax:
string[] columnNames = (from dc in dt.Columns.Cast<DataColumn>()
                        select dc.ColumnName).ToArray();
Cast is required, because Columns is of type DataColumnCollection which is a IEnumerable, not IEnumerable<DataColumn>. The other parts should be obvious.
Use
var arrayNames = (from DataColumn x 
                  in dt.Columns.Cast<DataColumn>()
                  select x.ColumnName).ToArray();
I'd suggest using such extension method:
public static class DataColumnCollectionExtensions
{
    public static IEnumerable<DataColumn> AsEnumerable(this DataColumnCollection source)
    {
        return source.Cast<DataColumn>();
    }
}
And therefore:
string[] columnNames = dataTable.Columns.AsEnumerable().Select(column => column.Name).ToArray();
You may also implement one more extension method for DataTable class to reduce code:
public static class DataTableExtensions
{
    public static IEnumerable<DataColumn> GetColumns(this DataTable source)
    {
        return source.Columns.AsEnumerable();
    }
}
And use it as follows:
string[] columnNames = dataTable.GetColumns().Select(column => column.Name).ToArray();
List<String> lsColumns = new List<string>();
if(dt.Rows.Count>0)
{
    var count = dt.Rows[0].Table.Columns.Count;
    for (int i = 0; i < count;i++ )
    {
        lsColumns.Add(Convert.ToString(dt.Rows[0][i]));
    }
}