You need to do a few things:
-- 1. Remove constraint and drop column
IF EXISTS(SELECT *
FROM INFORMATION_SCHEMA.COLUMNS
WHERE TABLE_NAME = N'TABLE_NAME'
AND COLUMN_NAME = N'LOWER_LIMIT')
BEGIN
DECLARE @sql NVARCHAR(MAX)
WHILE 1=1
BEGIN
SELECT TOP 1 @sql = N'alter table [TABLE_NAME] drop constraint ['+dc.name+N']'
FROM sys.default_constraints dc
JOIN sys.columns c
ON c.default_object_id = dc.object_id
WHERE dc.parent_object_id = OBJECT_ID('[TABLE_NAME]') AND c.name = N'LOWER_LIMIT'
IF @@ROWCOUNT = 0
BEGIN
PRINT 'DELETED Constraint on column LOWER_LIMIT'
BREAK
END
EXEC (@sql)
END;
ALTER TABLE TABLE_NAME DROP COLUMN LOWER_LIMIT;
PRINT 'DELETED column LOWER_LIMIT'
END
ELSE
PRINT 'Column LOWER_LIMIT does not exist'
GO