0-5V supply to control brightness of BWTek spectroscopy light source
The data sheet says: 


  Modulation Input DC 0-5 V to Set Output Power


Looks to me like the comment on 'matching' refers to the power supply rather than the control input. 

So you need a solid power supply capable of > 1.1A for the lamp and controller and an input signal suitable for a 3.5K input Z. 

A simple way to get that would be to use a 5V series reference such as a AD1582-85 from the 6V supply (needs to have a low dropout voltage), add a pot (say 10K) from 5V to GND and buffer the output with an op-amp voltage follower such as an LT1637 that can handle inputs down to the negative rail and to within 1V of the positive rail, and has output with 3.5K load that will get within 1V of the positive supply rail. Power the op-amp from the 6V supply. 

Damage is most likely to come from an incorrectly wired unit, or a power supply that is out of spec.