Are self-ordered lab tests tax deductible? I ordered them for a condition I have.

No, this would not change the answer.  You can deduct things such as a ramp, wheel chair, weight loss programs or modifications to your home that are necessary to treat or get around with a medical condition.   So the criteria to take a medical expense deduction is lower than that to use your HSA. 

Also, please note, medical expenses are only deductible for the amount that exceed 7.5% of your AGI.

 Itemized expenses include mortgage interest,  charitable contributions, state and local taxes up to $10,000, medical expenses in excess of 7.5% of your AGI and casualty and losses in excess of 10% of you AGI with the first $100 not counting towards the loss.  Your health insurance and all medical expenses are only deductible for the amount that is over 7.5% of your AGI.  This means if your AGI is $50,000, then the amount that is over $3,750 is deductible.  

Then your total itemized expenses would need to be greater than your standard deduction below in order to benefit from your medical expenses. 

The 2023 Standard Deductions are as follows:

• Married Filing Joint (MFJ)              $27,700
• Married Filing Separate (MFS)      $13,850
• Head of Household (HOH)             $20,800 
• Single                                                     $13,850                                

Blind or over 65 and MFJ or MFS add $1,500

Single or HOH if blind or over 65 add $1,850

Standard versus Itemized Deduction