ECL to Lemo connector
... it doesn't have lemo conncectors but ECL.


I think you have some misconceptions or misunderstandings here. ECL doesn't describe a type of connector but a standard for digital logic. 

The discussion of "ECLbus" in the datasheet you linked most likely refers to the digital interface for the ADC outputs than the analog interface for the inputs.

The analog input connector is simply described as "8x2-pin front panel connector (Ansley 609-1607). ." Which gives a complete vendor and part number that would (if the vendor was still in business) allow you to obtain the complete specs for this connector. Searching Octopart (for a header pn referenced in one of the other LeCroy models on that page), it seems that TE and some other vendors still cross-reference the part and it's a standard 2x8 header with 0.025" square pins on 0.100" spacing.


  In addition is it possible to make a home made connector? It the manual it is stated that the left input pin is the signal and the right is the ground. I feel that if I connect the core of the coaxial cable to the positive pin and the shielding to the ground I would be OK. Is this right or I have to reconsider?


This should work and is probably your best bet.