The LNAT begins its testing cycle late in the year (around September) and ends it sometime in the middle of the following year (around July). It can be taken only once per cycle — any additional sittings will be automatically invalidated — and its results are valid only within that academic year.
This means if you are applying to UCAS in 2021-2022, you must also take the LNAT during the 2021-2022 testing cycle, and should only be registering for a test date late in 2021, from September onwards. If you take the LNAT in the earlier half of the calendar year before the summer holidays, your result will not be downloaded by the universities and you will have to take the LNAT again at the correct time.
The LNAT test can be taken on any day that there is an appointment slot free at the test centre you have chosen. However, you do also need to ensure that you sit for the test before your application deadlines. As such, it is important that you register for the test early, so as to give yourself a higher chance of getting an appointment on the day of your choice, and do not have to worry about not having available test dates before your application deadline. Do note that Oxford tends to set their deadline fairly early (around October), so applicants to Oxford must plan to sit for the LNAT before then. For most other UCAS applications, your deadline will be sometime in January of the next year.
For Singapore University of Social Sciences (SUSS) specifically, because their applications close only in the middle of the year in July, applicants for the 2022 intake can take the LNAT between 1 September 2020 and 31 July 2021.