You gave the answer yourself. F-16 is not our baby made and manufactured by USA, therefore trainer required. JF-17 is our product hence trainer not required. Likewise Tejas is your product why you need a trainer for it.
Question you should asked, whether JF-17 dual seat is needed by Pakistan or it is needed for the export countries.
1. If PAF don't need trainer for JF-17, then it means that the pilot would be trained on the F-16 dual seater.
2. If the export countries are seeking dual seater JF-17, it means that JF-17 needs trainer version.
For you queries LCA Tejas don't need trainer for IAF because IAF already have HAWK advance trainer jet. However there are many advantages with the LCA trainer over HAWK trainer.
1. LCA trainer version will have bigger space for the fittment of the MMR (EL/M-2032), and HAWK trainer don't have space for such radar in its nose.
2. The LCA trainer is home grown product and could be customised, such as its digital cockpits could be programed in such a way, that it could mimic SU-30 MKI cockpit, and could be used for the training of the pilots of the MKI, reducing the cost of the training several times.
3. Those LCA trainer could be used in the combat mission, if the need arises, and could be used for the tactical interdiction role, and ground attack role.
4. IAF already is inducting LCA MK-1 in numbers -- 120 number, so the advancement of the avionics, and upgrades could be benifited by the trainer version too.
5. LCA program also have the MK-1 Naval trainer version too, which INAf could used for the carrier operation, thus reducing the training cost of the MIG-29 K and could be used in the costal area defence and survellance.
6. For the Ground attack role, the trainer version could be fitted with the IRST on its nose and NAV attack avionics.
and for the air defence role, the LCA trainer version could carry EL/L-2032 MMR.
P.S HAL too have one more product called Combat HAWK project which is the combat version of the HAWK trainer which HAL is developing with the JV with the BAE for the global market. So the LCA MK-1 trainer will have to compete with the Combat HAWK version too.