If I press my accelerator to the floor (trying to get up a hill or something) it's a bit slow to come back up which is scary. There's about a 1 second delay. I'm assuming the original grease from 1991 has hardened and become like peanut butter.

Is there some feasible way to lubricate the accelerator cable? (not the speedometer cable. I put that in originally but can't edit it)

Yes it is easy to lubricate. Pull the instrument cluster, unscrew the cable from the speedo, pull out the inner cable paying attention to which end goes to the cluster and clean the hardened grease off to it. Spray it with Würth HHS-K which is a great grease that is in a light carrier. After reinstalling the cable, spray plenty down the cable and you’ll be golden.

__________________
2014 GL450 76K - Wife's DD
2013 GL350 123K - My DD
2002 ML320 300K hard miles (workhorse)
2001 Z3 105K the 4 weeks a year ride
1995 E300D 189K - Rarer ALL options one ortho seats & all

Past ones
2015 XC70
2008 V70
2003 XC90 2.9 (POS)
1998 Wrangler (sporting a SBC 388)
1995 E300D 500K - Should have kept it!
1985 E300DT
1984 E300DT-T
1984 240D Gray market

Throttle or speedometer???

If you’re actually talking throttle, first remove the cruise control linkage. For whatever reason, cruise gets stiff, and can cause lingering rpm’s, if not big overshoots/over speeds for a short time as springs are bringing things back.

If the linkage balls are gummy/un-lubricated, that can affect things too.

__________________
Current Diesels:
1981 240D (73K)
1982 300CD (169k)
1985 190D (169k)
1991 350SD (116k)
1991 350SD (206k)
1991 300D (228k)
2008 ML320 CDI (199k)
1996 Dodge Ram CTD (442k)
1996 Dodge Ram CTD (267k)

Past Diesels:
1983 300D (228K), 1985 300D (233K), 1993 300D 2.5T (338k), 1993 300SD (291k)