Alice and the band were friends with Morrison in the late 60's. Jim was an influence on Alice as well. Alice explained that when Jim Died, instead of sending flowers, he wrote 'Desperado' for him. Using the analogy of rockstars as gunfighters while emulating the Morrison vocals on this song. Alice mentioned this during the '96 and '97 tours and on the 'A Fistful Of Alice' album.

Also Alice's line from 'From The Inside', "...raise a toast to Jimmys ghost..." is a Morrison reference.
(Renfield, January 1996)

Were Jim and Alice very good friends?

For awhile. They did lots of shows together in LA and hung out when Jim wasn't too crazy.
(Renfield, January 1997)

The line in the Doors Song 'Roadhouse Blues' (and covered by numerous bands) that goes "Well, I woke up this morning, I got myself a beer " is reputably about Alice.