As the name suggests, the Komodo is an island which houses over 2500 giant Komodo dragons in the Komodo National Park. There are travel agencies which offer 1/2 Day tour packages around Komodo dive center from Lombok.
If you wish to submerge yourself further into the beautiful Lombok culture, the Bertais Market is recommended. Bertais Market is an open air market where you can experience the truly Lombok culture. You will also be greeted by the wonderful locals and can use the opportunity to mingle with them. Mount Rinjani is the second highest volcano in Indonesia and trekking up will take up to 5 days. Other than enjoying the scenic views of the volcano, you can also experience the Rinjani waterfall.