Hi!
I'm new here, first I want to introduce my self, Im from Costa Rica and since one year Im the proud owner of a Series 3 diesel 88 from 1978 , my dad also have a 109 from 1964 (we have a lot of Landys here!)

I have a problem, months before I purchased a pair of Hella 4000 with the appropriate wiring harness form this band also. I followed the correct steps to install the harness but the lights dont worki am confused because we checked with a tester and there electricity on the plugs that goes to the lights
By the way i have a new battery with 950 EEA but the alternator is the original Lucas.

I appreciate very much your help!!

Having 12 volts doesn't mean there's enough current to light the bulbs.

Use a feed wire directly from the battery and work backwards from the bulbs, relay (assuming you've fitted one), switch to see where the problem is.

It could also be a poor earth.

Thank you!!.. Yes my wire is already connected to the positive of the battery, then to a 20A relay and then to the switch and lights. I also checked with the tester the earth of the 2 lights and the relay and they are good..I dont think can test the lights directly from the battery because there is not cables outside, only a female plug

Check you've got the right connections on the relay - there are wiring diagrams on this site. Is the relay clicking when you try turn the lights on? Is the relay coil fed from a switched feed (normally the headlight feed in the UK so the extra lights only come on with hi beam).
The extra switch goes between live and the relay coil - your description of the wiring is a little unclear here.