HELOCs fluctuate with the interest rate so you need to forecast if you have enough funds to cover yourself in the event of hardships where the interest rate rises, rental rates drop, vacancy rates increase etc. 

Now I purchased this house for $48,000 and I can actually increase the rent on two of the Units, but putting that aside, $1,475/$48,000 = 3.07%.

If it averages $50 a month, reduce the rent for Tenant A by $25 and increase the rent for Tenant B by $25.

Most of the time, people who get a raise/second job or more income from any source, wind up increasing their spending and up their standard of living and never actually use that money to pay debts off.

As you scale your business it will become increasingly more difficult to allocate your expenses to the proper rental or business if expenses are running through your personal account.  

My question is as the new owner, does that lease still have to be honored by me or can I redraft a lease (with a lot of the same stipulations) but giving them 60 days notice of a increase in rent?

You would be better off to shop for a new manager to increase the income from the property prior to the sale.

While it was a lot of work we were able to customize the "owner's unit" to our liking, and the work we did to the other unit allowed us to increase the rent.  

There is plenty of room to increase rents and it has two newly renovated units.

The owner's own contractor even backed out. 2- My rent where I am currently living will increase significantly (by $250) in about 2 months.