Yamaha dtr125 starts then cut out seems like battery

Hi just because the lights work does not always mean the battery is ok. It takes a lot more power to crank the starter.
Generally that clicking will be either the battery or the starter motor. I would suggest if you can try jump leads and if it starts problem is battery, If not problem is most likely starter motor. For a possible third thing to check Make sure the battery leads are tight.
Cheers Mike;-)

Check your starter. It sounds like this is the culprit.

Rechecked all battery connections? Check the fusible link or links in the wiring around or near the battery, maybe off the fender mounted relay. Fusible links are old time variants of regular fuses. If they burn out, they can be cut out and replaced. As part of the power distribution, they are near the battery source.

first check the starter relay it could be faulty,,,then check the starter motor,,that could also be the fault,,,my gess is its the motor?

Charge battery to full, start in neutral, still clicks? Bad ground, or bad connection. Jump starter solenoid with screwdriver,etc. if motor turns over the relay is bad. Chaz Moto DC

Sounds like a problem with the starter, could be a starter fuse, relay or solenoid. The start cicuit wiring could also be damaged. If you can pull-start the motor, and it runs fine, you have pretty much eliminated any problems with the motor. Check the wires running from the start button make sure they are intact, also trace them and look for around a 1" cubed black box. This is the relay, when you push the button, if its working, you will feel the box click. Also locate the starter and do the same thing. If you feel or hear the starter click, the solenoid is working. The battery voltage could also be too low to energize the starter motor. Could also be a battery or alternator issue. Check the battery voltage and for any sounds coming from the bike when you push the start button.

air gap on electronic ignition or tdi unit or carbs want cleaning

hope this helps.