My understanding is that the ECC33 is a very close match to 6SN7 and can be used safely in a Lyr 3 (I've run quite a few for quite awhile in mine).
The ECC32 (probably best known for the Mullard coke-bottle shaped tube) has different electrical characteristics (somebody here can elaborate I'm sure) that make it a bit risky to use in a Lyr 3. That being said, I've used a couple in my Lyr 3 (the Mullard coke-bottle one and a Cossor ECC33) without any problems.
The ECC32 uses 0.95 amps of heater current (regular 6SN7 uses 0.6 amps, so just over 50% more). Seems a bit risky as the Lyr3 is built for 6SN7 standard, but nice to know that it seems able to handle it

The ECC33 on the other hand, uses only 0.4 amps so it certainly is safe to use and might even have the Lyr3 running a bit cooler than usual

ECC33: https://www.radiomuseum.org/tubes/tube_ecc33.html
ECC32: https://www.radiomuseum.org/tubes/tube_ecc32.html