I went through the list of LiChess classical top 200 players and collected the FIDE ratings of LiChess classical ratings of anyone who I could verify on FIDE's website as actually having a FIDE rating:
LiChess FIDE LiChess username Name
2585 2265 ClassyPlays Thibault Dudognon [FM]
2389 1869 nikkon2006 Nikita Konstantinov
2373 2274 PchelkinVK Andrey Ermolaev [CM]
2357 1780 LeProfessionnel Xavier Bohaer
2329 1963 Callmoon Lina Nassr [WIM]
2299 2249 Peristeria Marcus Schmuecker
2290 2214 Crocodilu1976 Adrian Stanca
2278 1899 TonoyanRob7 Robert Tonoyan
2271 1900 CamelClutcher Daniel Herman
2269 1985 Chess-For-All Alexey Pugach
2242 2242 weichi Eugeny Pankin
2241 2208 kirillgenius Kirill Shcherbinin [CM]
2241 2247 Cizar Srboljub Zaric
2236 2065 pepellou Jose Doval Gonzalez
2235 2093 Suleymanov_Marat Marat M. Suleimanov
2232 2155 Son_Of_Caissa Hrvoje Vlahov
2228 2358 VadimCernov Vadim Chernov [IM]
2221 2010 emiliooo Emilio Profili
2219 2274 Josip_buje Josip Bulic [FM]
2214 1455 diarbovi Diego Armando Bonilla Viamonte
2206 1878 hebertvr Hebert Valera
2199 1958 MrsBlunderqueen Jan Oltmanns
2193 2215 aconeni Ondrej Toman
2193 2187 teddyhh Julio Fernandes
2187 2190 yichen Yichen Han
2181 2298 jolle23 Johan Hultin [FM]
2171 2270 Konnov_Oleg Oleg Konnov [FM]
2164 2138 FrankDischinger Dischinger Frank [FM]
2162 1754 moldscaien1357 Dimitrios Makridis
2145 1898 shayanaghaie Shahram Aghaei
(I use the current FIDE rating, not the one listed on the LiChess profile; this affects 6 players. One player had a FIDE profile page, but no rating: LiChess (2174); FIDE.)
We see some major differences in several cases, so we cannot expect a simple relationship between the two. However, perhaps it's fair to conclude that a typical low-2000s FIDE player could likely reach a 2100+ LiChess classical rating. However, I feel like it depends heavily on how seriously they play on LiChess.
Here's a plot of the above data, with a linear regression. It's an incredibly weak correlation.