If it's working with LR, and you're not RX'ing at -15 dBm on each side, don't worry about it.  The documented Rx minimum for 10GBASE-LR is -14.4 dBm.  So if you're at -13 dBm or higher, you're fine.  If you're at -15 dBm, then you should swap them for ER.

It's not an issue of efficiency.  It's about laser power and span loss.  ER transmits with more power, and its loss budget is better.  We budget to 0.35dB/km for 1310nm (LR), but only 0.25dB/km for 1550nm (ER and ZR).

In my experience, the conservative 10km and 40km (and 80km) limits are given for two reasons:

1. Dummy-proof the engineering.  We usually know the span lengths.  We don't always know the span loss.  This also lets us ignore chromatic dispersion.

2. Limitation of liability.  If it's 11km or 41km and it doesn't work, Cisco can always fall back on the specs.  That said, TAC never asks what the distance is.  They just check the RX levels.

Again, in my experience, span loss is what matters.  I have successfully used LR optics on clean fiber spans significantly exceeding 10km.  As long as you're above the minimum RX value, it will work.

Aside: 10km to 40km is a wide range.  I get a lot of success (and save a little money) in the middle of this range (15-30 km) by using ER on one side and LR on the other side.  You don't need to match the optics.  Again, being above the minimum RX threshold is what's important.

***Yes, I know that it's important to consider dispersion, but I've never seen CD be as significant as span loss until we exceed 80km on G.652 fiber.