Go for LSE. FAST is only renowned for its CS program, otherwise, the job market and the standard of studies at LSE for BBA/BSC is much better and it is usually the second choice of students after LUMS.
Go for LSE. Apply as a fresh men next year, transfer is a 1% chance. Wasting a year for LUMS wont harm you. Good news : Lums has increased their intake, so hit their LCAT and you'll have a fair chance.
Students joining any university thinking they'll transfer later to another uni, are going in a wrong direction! Transferring credits between Universities in Pakistan is not that easy, rather it's very very rare I would say (specially if ur looking to transfer to a higher merit uni, e.g LSE to LUMS)
Please do not risk ur future in the hope of this transfer!