Is it even possible?

I lost 15 pounds since January then gained 4 pounds and I am back up to 141 pounds.  I really wanted to be 125 by the end of May for the Memorial Day Picnics I will be attending.  Is it possible to lose 16 pounds in two months in a healthy way?  I don't workout but maybe it is time to start.  I am 5'4" and have a medium bone frame.  I am 28 years old.  What do I need to do to make this work?  I reeeeeaallly want it to work this time.

Yep, it's absolutely possible. That's about 2lbs a week, which is the maximum reccomended rate of weight loss. You need to have a daily calorie deficit of 1000, so if you eat 1500 calories and burn 2500 calories, you can do it.

With your statistics, losing 16lbs would be a stretching target because it's more than 10% of your current body weight.  Aim instead for 8lbs in 2 months and be happy if it's more.  If you exercised daily and consumed about 1300-1400 cals a day you could easily hit 8lbs+

It's definitely doable.  Just make sure you are sensible with your calories and pay attention to the deficit (as birdy22 mentioned).  Working out may give your metabolism a great boost!  I never used to exercise, however when I started counting calories and exercising, I was shocked to see that I lost 10 lbs in the first month :-)  To give you an idea...I started out very slowly at once per week for half an hour (Because I hate being on the treadmill...but that's my only option) and made sure that if I did work out, that I gave myself a very challenging work out.  I moved it up to 2 days per week and the weight came off at 2 lbs a week.  When I stop working out, the weight loss slows to about 1 lb a week.  

If you work out a couple of days a week, you can definitely reach your goal.  Just make sure you are challenging yourself and that you make yourself sweat.  Also, don't forget to tone up!  A little muscle can make you look very slender + the more muscle you have, the more calories you burn.  Additionally, make sure you eat well and that you have a good amount of protein and complex carbs so that your body has the fuel it needs.  Good luck :-)