Does the r11e-lte have an on module antenna or does it need to use the U.FL connectors on it and use an off board/external one?

no internal antenna in the module, if that’s the question. You for sure need to use a U.Fl to SMA/whatnot adapter to an external antenna.

But any Mikrotik router that says LTE, includes the module and small internal antenna.

While it available as part separately, it be hard to use without a RouterBoard since they aren’t generic modules. So more for board products like RB953 or RM33. Those board do not have antennas so on those you’d need some u.fl pigtails and external antenna.

Got an antenna lead in the post shortly after posting which solved the issue. But I have the mini pcie module in a USB adapter and it works ok.