Firstly if you are talking about lattice attack please be very carefully with definition ot this type attack:)
becouse there is no one "definition" for lattice attack.

Lattice attack can be used only then if we define what we want to take as result. WE have a lot of "lattice attack" types like: CVP, SVP Doubled CVP, and of course mysthic "SLE method". 

all of this lattice attack is designed for something to find. YOU CANT USE "codes" and put there r,s,z without some "modification" to algorithm and waiting for good result.

 
here example:

1.) if we have 1 transaction with remarks:
 privatekey up to 128 bit : with nonce up to 128 bit -> lattice attack will show privatekey

2.) if we have 100 transaction with remarks:
 privatekey up to 2**20 bit : with nonce up to 253 bit -> lattice attack will show privatekey

3.) if we have 480 transaction with remarks:
 privatekey up to 2**10 bit : with nonce up to 254 bit -> lattice attack will show privatekey

4.) if we have 10 transaction with remarks:
 privatekey up to 2**200 bit : with nonce up to 240 bit -> lattice attack will show privatekey


what can we deduct? lattice attack is only bounded result depends the range of privatekeys.

second problem "if you will use" CVP againts SVP you will be have another values.