Is it legal for a business owner to a business Line of Credit for a personal investment?

That depends.  What are the terms of the lc?  Does the business owe money to other creditors and if so what are the terms of the contracts with those creditors?  Are there other owners of the business and if so what are the terms of the agreements between the owners?  The bottom line is that if the terms of the lc allow drawing on it for personal reasons, it doesn't violate any of the agreements with other creditors and doesn't prevent any of them beins paid, and it doesn't violate any agreements with any other owners, I see no reason why it wouldn't be legal, but it may still be problematic because the commingling of personal and business finances may allow a creditor of the business to "pierce the corporate veil" (assuming that the business is a corporation or other separate legal entity)  and hold the owner personally responsible for debts of the business.