For years I have used valve oil on my 3rd valve slide instead of grease. My normal routine is to clean it well about once a week, put on some slide grease and wipe that off nearly dry, then use valve oil when reassembling. I oil it daily along with valves, and repeat the cleaning weekly.
Since I haven't seen this mentioned before, I have to wonder... am I alone? And if so (or not), am I in danger of doing any damage to the slide? I have always preferred the slide to move as quickly and easily as a valve, and this accomplishes that.
Interestingly (or not), I have also always just used grease on the first valve slide. Perhaps because it has to move a much shorter distance, or perhaps because my thumb is much stronger, or perhaps because it is used much less often. I'm not sure.