Lertap uses Cronbach's coefficient alpha as its reliability estimate.
At times split-half reliability estimates may be useful, such as that found by correlating two half-tests.
For example, the half-tests may be created by splitting out the odd-numbered items as one half, and the even-numbered items as another half.
To see how to split a test into halves with Lertap, and correlate the halves, please refer to this topic.
A related topic having to do with assessing reliability has to do with "parallel forms", a situation where two tests designed to measure the same thing are developed simultaneously. At times these tests will have some common test items, at times they will not. They're called "parallel tests" as they can be used, ideally, interchangeably.
An interesting example of a parallel-forms development project may be seen here. Of added interest in this project was the use of a mixture of test items, multiple-choice and constructed-response.