Was there any use of scoring rules in economics or finance before Hanson published about LMSR?
Hanson wasn't the first one.

"Scoring rules and the evaluation of probability assessors" by Winkler was published in the Journal of the American Statistical Association in 1969 wasn't published in an economics journal but already mentioned economic applications.

Other examples (probably also not the first publications in economics journals, but still earlier than Hanson) are:

Selten (1991), "Properties of a Measure of Predictive Success?" in Mathematical Social Sciences.

Selten (1998), "Axiomatic characterization of the quadratic scoring rule" in Experimental Economics.