Please confirm me for this small confussion. Can I use non-insulated 600V terminal lug to be used for 11kV arrester circuit ? In my opinion Yes, since voltage will effect to insulation material only so for non-insulated doesn't matter.
Your basic understanding is not wrong, however in the USA many single conductor lugs are UL listed for only 600V. UL (or equivalent) listing is very important in North America. This perhaps is more to avoid liabilities from misapplications, than anything else.
Some manufactures say on their product datasheets that it is UL listed for 600V and 'recommended' up to 35 kV and with due warning that for higher voltage applications it must be used in conjunction with appropriate stress control termination kits/methods, in accordance with manufacturer's recommendation.
If the installation is all overhead using bare conductors, the metal is metal, it has no voltage rating per say.
You should consult the lug mfr. for their recommendations.
It depends on your application of the lug. During HV testing, a lot of testing is performed with 600V conductors in free air at voltages >22kV using normal 600V connections.
For a permanent installation, you should do the research with vendors.