I'm using the NI6509 and NI 6509e. According to the specifications, the minimum input voltage is 2V.
Does it mean, I can input a LVTTL signal (3.3V) ?
Is it recommended to use it like that? The alternative is to use a circuit to convert LVTTL to TTL, but, obviously, I'll be happy not to do it if not necessary.
You should be able to use the LVTTL signal directly as 3.3V is above the 2V minimum that is required to register as a logic high for an input.
I believe you shouldn't have any issues with using the NI-6509 to read a LVTTL signal. Just to be clear though, our device will not read a Logical high value until the voltage is above 2 Vs. I believe that since you have about 1.3Vs of clearance from this threshold you shouldn't run into any issues.
If you do notice issues with this, converting this to a TTL would be a good solution as well.