In box 14 on my wife's 2015 W-2, what does "LST" and "PA SUI" mean?

LST = Local Services Tax

PA SUI = Pennsylvania State Unemployment Insurance [premium]

http://www.newpa.com/local-government/local-income-tax-information/local-services-tax/

Are you able to deduct this on your Federal tax return? If so, where?

Box 14 on a W-2  is where employer's make notes for you.  They don't generally affect your tax return.

 

Click this link for more info on Box 14.

I live in Pennsylvania. I hope that someone in PENNSYLVANIA / PA can answer this.

I have always  itemized my taxes. My former accountant would itemize my Pennsylvania State Unemployment Insurance tax. 

That number was in Box 14 listed as PA SUI which I believe is a tax?

That number was then transferred /listed on Schedule A line 6. Does TurboTax automatically give me credit for this

YES!!

 

Enter Box 14 and be sure to select "Pennsylvania Unemployment tax" from the drop-down

The tax will be listed on Schedule A and included as a deduction if you Itemize Deductions.