With the help of Ben's superior document reading skills, I believe this is possible using the posterior() function.
library(topicmodels)
data(AssociatedPress)
train <- AssociatedPress[1:100]
test <- AssociatedPress[101:150]
train.lda <- LDA(train,5)
(train.topics <- topics(train.lda))
# [1] 4 5 5 1 2 3 1 2 1 2 1 3 2 3 3 2 2 5 3 4 5 3 1 2 3 1 4 4 2 5 3 2 4 5 1 5 4 3 1 3 4 3 2 1 4 2 4 3 1 2 4 3 1 1 4 4 5
# [58] 3 5 3 3 5 3 2 3 4 4 3 4 5 1 2 3 4 3 5 5 3 1 2 5 5 3 1 4 2 3 1 3 2 5 4 5 5 1 1 1 4 4 3
test.topics <- posterior(train.lda,test)
(test.topics <- apply(test.topics$topics, 1, which.max))
# [1] 3 5 5 5 2 4 5 4 2 2 3 1 3 3 2 4 3 1 5 3 5 3 1 2 2 3 4 1 2 2 4 4 3 3 5 5 5 2 2 5 2 3 2 3 3 5 5 1 2 2