Applying grease to CD player mechanism

I need to apply grease in a CD reader mechanism of an old discman and I have a few questions about it.

OBS: I'm posting it here since it was rejected from r/AskEletronics by being too off topic. I also posted on r/techsupport, but I'm not so sure if it's the right place either.

  1. I've read that I should use a lithium based grease or silicone grease. Does it make a difference and how so?

  2. In case I use a lithium based grease, does its color make any difference? I found one being sold as "blue lithium soap grease", and the compound is indeed blue, but saw someone saying some other color should be used, hence the question.

  3. Should I try cleaning the mechanism for remaining grease before applying the new one?

  4. In case I apply a grease that it's different than the grease it was originally applied (e.g. I applied silicone based where originally it had lithium based) so they end up being mixtured a bit, will it be bad?

Thanks in advance.