KKL will work fine on the 156 you dont need anything more than that, would think 159 will be same but ELM interfaces from what I have read do more and can perform more functions.
I think you said you have a 159 1.9 jtdm Lusso which should be the 16v jtdm motor, so here you see, from FiatECUScan website:
Bosch EDC16C39 CF4/EOBD Diesel Injection (1.9, 2.4) |INFO|DTC|PRM|ACT|ADJ| KL ELM OBDKey
you can read ECU info,DTC which is error codes, and the rest is parameters, actuators and adjustments all using KL line, ELM cable or OBDKey, so KKL should work.
however if you look at all the other functions available for your vehicle (which you should note you require the paid version of FES for, you can only talk to your engine ECU and get CANBUS info on free version) require ELM or OBDKey:
AISIN AF40-6 Automatic Gearbox |INFO|DTC|PRM|ACT|ADJ| KL ELM OBDKey
TRW Lucas ABS |INFO|DTC|PRM|ACT| KL 1ELM 1OBDKey 1 A1
TRW Lucas ABS (ESP) |INFO|DTC|PRM|ACT|ADJ| KL 1ELM 1OBDKey 1 A1
TRW MY03 Airbag (2F-2P-2L-2T-1G-I) |INFO|DTC|PRM|ACT| ELM OBDKey
TRW MY03 Airbag (2F-2P-2L-2T-2G-I) |INFO|DTC|PRM|ACT| ELM OBDKey
Service Interval Reset |INFO|ADJ| ELM OBDKey
Lauberhorn Convergence C1 (Blue&Me Nav) |INFO|DTC| ELM OBDKey
Marelli Connect (NAV) |INFO|DTC| ELM OBDKey
Marelli/Microsoft Convergence (Blue&Me) |INFO|DTC| ELM OBDKey
Marelli/Microsoft Convergence C3 (Blue&Me Nav) |INFO|DTC| ELM OBDKey
Siemens Instrument Panel |INFO|DTC|PRM|ACT|ADJ| ELM OBDKey
CAN Info |INFO| ELM OBDKey
CAN Setup / PROXI Alignment Procedure |INFO|ADJ| ELM OBDKey
Marelli Body Computer |INFO|DTC|PRM|ACT|ADJ| ELM OBDKey
Delphi climate control (Dual/three zone) |INFO|DTC| ELM OBDKey
Delphi climate control (Single zone) |INFO|DTC| ELM OBDKey
Litronic XENON headlamp (left) |INFO|DTC|PRM|ACT|ADJ| KL 12ELM 12OBDKey 12 A1
Litronic XENON headlamp (right) |INFO|DTC|PRM|ACT| KL 12ELM 12OBDKey 12 A1
Boot (G.E. PROCOND) |INFO|DTC|PRM|ACT| ELM OBDKey
Driver's Door (G.E. PROCOND) |INFO|DTC|PRM|ACT| ELM OBDKey
Passenger's Door (G.E. PROCOND) |INFO|DTC|PRM|ACT| ELM OBDKey
Valeo parking control |INFO|DTC|PRM|ADJ| ELM OBDKey
you will note that some of them say ELM and then a number, like ELM12, these mean than you need an adapter cable or need to modify your cable to view a different ECU pin on the multi-plug.
all info freely available on FiatECUScan website, hope this helps.