I have a TRD 1.5 way LSD the noise is normal for a mechanical lsd just make sure you have good oil in it. does it go away as you corner faster?
mine makes a racked at only parking speeds.
you should hear the noise up to a point, then you will hear your tyres sorta skipping...... if that makes sense.
i seriously doubt that mismatched tyres would bugger your diff it would make the diff work harder though.
I am using penrite 80w/140 atm
just make sure it is a good lsd oil
and btw there is a running in period and your diff place should be geting you to come in after that to have the oil changed, my recommended run in period was 400 kms.
If you hearinf funny knockinf sounds check the wheel nuts as you may have a loose wheel .... sounds funny but i had that happen to me when i went to a certain place..... never going there again.