I'm in Lakeland. There are some triathletes that swim at Gandy Pool, you can find them there Mon, Wed, and Fri mornings at 5:30 am
(be forewarned, it is quite crowded and you may have to wait for a lane
), admission is $3, but you can buy 20 admissions for $40.
There are three great bike areas, Lake Hollingsworth, while it is repetitious you can do some great speedwork around the lake.
Also, for longer rides, hit Van Fleet trail in Polk City,
http://www.dep.state.fl.us/gwt/guide/regions/eastcentral/trails/gen... The trail is 29 miles long, so you can ride as far or as short as you need to. There are only two water points, one at 10 miles north of Polk City trailhead and one at the very north end of the trail in Mabel. So two bottles and a Camelbak are recommended.
The other trail is Fort Fraser Trail
http://polktpo.s3.amazonaws.com/downloads/45/Fort_Fraser_Trail.pdf It is almost 8 miles long, and there is a water station about 3 miles south of PCC, plus there are several stores along the way you can hit and buy water or Gatorade.
As for runs, Hollingsworth is also a great run spot, Lakeland's own runner's store FITniche has a water station by the parking area on the southside of the lake. Also, many runners will run around the lakes downtown:
http://www.mapmyrun.com/run/united-states/fl/lakeland/72438682
Most weekday nights you will find me on Hollingsworth, I have a red and silver Cervelo and usually wear a black and blue Giro aero-helmet
(although I had to take August off of the bike, but I will be back in early September
).
Good luck to you on your tri-journey.