Depends on the light novel. There are some light novels at
Jコミ. (Also manga and ４コマ). This is a free (ad-supported) site for older works - lots from the 1980s/1990s. I picked out the first couple on the list and quickly transcribed the first bits as an example (may have errors):
First is 妖精作戦
徹夜明けの目に、朝の日差しが痛かった。榊裕（さかきひろし）は目をしばたたかせながら新宿駅東口の大時計を見上げた。電光式の文字盤は五時三十分をまわっている。
「学校へ戻って寝れるな。ふわあ」
榊は大きくあくびをして背伸ばした。眠い。
「八本...じゃない、九本か...」
榊は前日の朝から見た映画の本数を数えなおした。夏休みの最後の日に、見逃がしていたロードショーや二番館に転げ落ちた作品を追いかけて、あげくの果てにオールナイトを二つハシゴした収穫である。
「あーつかれた」
新宿アルタ生面の横断歩道をのったり渡って地下道に入る。早朝だけあって人影は少ない。
There are a few non-教育 kanji here but some of them are understandable from context. More to the point, you don't necessarily need to know every word/kanji here to understand what's going on. 二番館 is, I'd argue, not obvious from the 'meanings' of the kanji, but obvious enough from context if you knew the much more common word 映画館.
Second one on the list was 愛の武将―直江兼続
天正五年（一五七七）春、越後の夜空に浮かぶ月は、標高六十三丈（約一八九メートル）の春日山の姿を、くっきりと照らし出していた。三月の十三夜の月は、ぼんやりとした霞をまとって、咲き始めた八重桜を照らし、春の終わりが間もないことを告げていた。新暦の四月十一日にあたる。
城下で暮らす民も、ここ数日の暖かさですっかり身体の働きも軽くなったように、樋口与六兼続（ひぐちよろくかねつぐ）は感じていたが、春日山城内は緊張感に包まれていた。無駄なく働き回る兵士たちの活気に溢れた声が、夕餉（ゆうげ）の前まで続いていた。二日後の十五日に織田との戦（いくさ）に向け、進軍が始まろうとしていたのである。
Although these are both labelled 'light novels' this one is pretty clearly more difficult. It has more out of 常用 kanji, some of them (溢, 霞) presented as vocab without furigana. It assumes some degree of cultural knowledge (terms like 越後). The style appears to be slightly 'heavier' overall - it may just be that they're trying to set the scene/tone with the opening lines, but it's likely to have more chunks of descriptive text.
It's probably not that difficult for someone who has an interest in history and knows some of that vocab, and is familiar with the typical "ye olde time" fake old Japanese the dialogue is almost certainly going to be written in (I didn't check), but I would consider this one more of a slog, and the first one lighter reading.
It's not a matter of X number of kanji or Y number of words - that's like saying there's a set number of words of English you need to know to read a novel in English. But someone who has a reasonable level of vocabulary/grammar knowledge and something around a thousand kanji should be able to find a light novel they can handle.
