I do reside outside Pakistan so i filled out the online application form they didn't say anything about the admission test, just asked me to fill out my SAT scores. The mail here is usually delayed by a month or two, how did u get ur letter was it through express or regular mail?
The procedure worked this year (roughly) like this.
1. Around mid of April, they start dispatching admissions offers in the 'first' merit list. These candidates were not invited for an interview and had a direct admission conditional on payment of the first semester fees by a set date and achieving certain grades in their A-Levels.
2. The deadline for SSE admission payment was 2nd May. 100% refund was possibly up till 17th May, hence the institute waited for any number of candidates that decided to opt out, to opt out, so that they learn the number of candidates they need to complete the batch. Like, there were 200 students in the first merit list for SSE. It's likely that about a 100 didn't pay the admission fee or withdrew it, so now the institute needs to make up for the other 100 students.
3. These days they are dispatching letters for those in the second merit list. They are being invited for interview and successful candidates will make up for the deficit.
4. They might make a third merit list if the deficit is significantly incomplete.
5.
Additionally, if some students don't attain the minimum grade requirements in their A-Levels, their is a 'clearing' where further students would be invited to join LUMS incumbent on interview.
Letters are sent through express mail. Insha Allah you might receive an interview invitation if you are in are in the second merit list. Since you're abroad, it might take more time.
How I know this: I was offered admission without interview mid-April and one of friends has received a letter late May which invited her for an interview on 5th June. Also, I joined pieces of what other people experienced and suggest this is how this works. I might be wrong.