The tax return determines what you owe in tax or what you get back as a refund.
First you enter all your income, you say that was 15,000 in your case.
Next that income is adjusted (things are subtracted out). There are various things that can adjust the income, but let's just use the Standard Deduction which most taxpayers take. 13,850 is the amount of the Standard Deduction for a taxpayer filing Single. Subtract 13,850 from the 15,000 total income leaves 1,150 as taxable income. If you are in the 10% tax bracket, that would be 115 tax, but you must have other adjustments that brings the tax down to 71, perhaps interest on a student loan. Look at line 15 on your 1040 for your taxable income and line 16 for your tax liability. Look at Schedule 1 for adjustments.
As stated earlier. The Lifetime Learning Credit is Non-refundable, so once that tax is brought down to zero (line 22) the Lifetime Learning Credit ends.
From there, additional tax MIGHT be added which the Lifetime Learning Credit cannot offset, such as self-Employment Tax. The final tax liability is on line 24.
After that, your payments (withholding and estimated payments) as well as REFUDABLE credits are factored in for the final tax bill or refund.
Since you said the Lifetime Learning Credit was 71, it can be assumed that was your liability (or close to it) on line 16.
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