First, there is no LT235/80R16 - and this fact causes all sorts of discussion.
It is likely that you can replace your ST tires with a larger LT235/85R16, but you will need about an inch more clearance around the circumference.
Some folks have pointed out that an LT245/75R16 is closer in diameter to the ST 235/80R16, but they frequently forget to point out that it is wider by 5/8" when mounted on the same wheel - AND - it requires a minimum of a 6 1/2" wide wheel.
Then there is the issue of load carrying capacity. An ST235/80R216 Load Range E has a maximum load carrying capacity of 3420# at 80 psi, while an LT235/85R16 LRE is 3042 # at 80. (same for the LT245/75R16 LRE).
There is one school of thought that says you need to replace those ST's with something of the equivalent load carrying capacity - and that means a Load Range F (3415# at 95 psi) or a Load Range G (3750# at 110 psi.) - which are kind of hard to find.
With that approach, there might be an issue will the wheels - although some say that the load is what is important and the inflation pressure not so much - that if push came to shove, it would be preferable to use more inflation to get the load carrying capacity in the tire. In other words, which would be worse, not enough load carrying capacity in the tire or exceeding the inflation pressure limit of the wheel? In either case, there is a risk of failure - and it can be pointed out that we are aware that tires fail regularly, but we are unaware of any recurring wheel failures.
But there is another school of thought that says that an LT235/80R16 has a larger load carrying capacity because it is speed restricted to 65 mph - and that if you use an LT235/85R16 in its place(which is not only larger in diameter, which equals larger load carrying capacity, but also has a much higher speed rating), it is actually a step up in load carrying capacity.
You may find tire dealers who would refuse to mount an LT tire in place of an ST tire - a problem you can avoid by having the tires changed individually.
Now this topic is quite the source of discussion. I hope I have covered the issue without bias. The choice of how you want to look at this is up to you.