Generally speaking, any oil that meets the quality standards of an SF, SG, SH, SJ, or higher rating can be used in your riding lawnmower. There are a few reasons why specific oils are recommended more often however.
The LT2000 series mowers use several different engines and your profile included no model number to confirm which you have. But all the motors used in that series are manufactured by Briggs & Stratton and they recommend their 30W oil for all of them when used in temperatures above 40 degrees Fahrenheit.
The main reason for this is the fact that these engines are air-cooled. An air cooled engine will generally run at a higher temperature than a liquid cooled automotive engine and runs larger tolerances between the engine parts to compensate for this and still keep the engine reliable and affordable.
A 30W oil is a single-weight oil while most automotive oils are multi-weight, such as a 10W-30. The weight rating is based on several factors but, essentially, the heavier weight an oil is the thicker it is. Heavier, or thicker, oil like 30W can handle higher temperatures and loads while still protecting and lubricating the engine components. Lighter, or thinner, oil like 10W creates less drag and resistance so an engine starts easier and components are better protected and lubricated until the engine temperatures rise.
Multi-weight oils go through extra processing that allows them to act like thinner oil in low temperatures and still provide the protection of thicker oil when temperatures rise. That extra processing generally makes them more expensive but compared to a single-rate oil like 30W it helps cars start more easily and reduces internal engine drag to increase fuel economy as engine speeds and loads vary repeatedly during typical driving.
In an air cooled application like your mower, which is generally run at a steady throttle rate and where operating temperatures are higher overall, a multi-weight oil has fewer benefits but can still provide as much protection as a comparable single-weight oil. However, a multi-weight oil is thinner overall than a comparable single-weight. For example, 10W-30 oil protects the same as 30W oil at higher temperatures but it is actually thinner overall to allow it to act more like a 10W oil in colder conditions.
And that is the negative part of using multi-weight oil for your mower. Using multi-weight oil in your mower engine will result in higher than normal oil consumption. The larger tolerances between components in your air cooled motor are necessary and work fine with a 30W oil but will allow a thinner multi-weight oil, such as 10W-30, to bypass engine components and be burned along with the fuel and air going through the engine. Not only does that add to the environmental impact, but the oil costs you more and you need to use more of it.
If you are using the riding tractor in cold conditions, below 40 degree f, then a 10W-30 or even 5W-30 is recommended to compensate for the higher drag and wear that occurs trying to start an engine at such a low temperature and still provide protection once the engine warms. For most other applications though, you are simply buying more expensive oil, and burning more of it, than you need to be.
There are also automotive oils out there that are Synthetic. These go through even more processing than a regular multi-weight and are even more expensive. Their advantage in automobiles is to provide even better protection across an even wider operating range than a standard multi-weight does. Often these oils boast longer intervals between oil changes to offset some of their cost.
Synthetic oils will work in your riding lawn mower and generally increase oil consumption less than a regular multi-weight does. However, the conditions where Synthetic oils claim to add protection, and therefore increase oil change intervals, are not typically present on a riding mower. So Briggs & Stratton do not recommend increasing the oil change intervals for your mower when using a Synthetic oil. And, once again, you will spend more to gain features that your riding lawn mower simply will not need under normal operating conditions.