The Lifted Index is found by comparing the temperature of a parcel of air raised from the surface to the 500 mb level to that of the actual temperature at 500 mb. If the parcel temperature is warmer than the actual temperature, then the Lifted Index is negative and the troposphere is unstable relative to surface based convection. A parcel that is warmer than the surrounding environment will be less dense than the surrounding environment and thus the parcel will want to rise just as a helium balloon rises in the air.
There are three important components that make it more likely the parcel temperature will be warmer than the environmental temperature when a parcel is lifted from the surface to 500 mb. These three components are the surface temperature, the surface dewpoint and the actual temperature at 500 mb. The LI will be made less stable by either increasing the surface dewpoint, increasing the surface temperature and/or decreasing the 500 mb temperature.
Increasing surface dewpoint: Increasing the surface dewpoint enables more latent heat of condensation to be released and thus this allows the parcel to be warmer than it otherwise would have been once it is lifted to 500 mb.
Increasing surface temperature: Increasing the surface temperature causes the temperature of the parcel to be warmer than it otherwise would have been once it is lifted to 500 mb.
Decreasing 500 mb temperature: If the 500 mb temperature cools, then it makes it more likely the parcel will be warmer.