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from Astrometric Solar-System Anomalies of Anderson and Nieto, 2009, page 9,

Increase in the eccentricity of the Moon's orbit

While the mean motion and semi-major axis rates of the lunar orbit are consistent with physical models for dissipation in Earth and Moon, LLR orbital solutions consistently reveal an anomalous secular eccentricity variation. After accounting for tides on the Earth that produce an eccentricity change of $1.3*10^{-11} yr^{-1}$ and tides on the Moon that produce a change of $-0.6*10^{-11} yr^{-1}$, there is an anomalous rate of $(0.9\pm0.3)*10^{-11} yr^{-1}$ , equivalent to an extra 3.5 mm $yr^{-1}$ in perigee and apogee distance (Williams \& Boggs 2009). This anomalous eccentricity rate is not understood and it presents a problem.

On the anomalous secular increase of the eccentricity of the orbit of the Moon, by L. Iorio, 2011, explores several alternatives to explain the problem. All of them were inviable, concluding:

Thus, the issue of ﬁnding a satisfactorily explanation for the anomalous behavior of the Moon’s eccentricity remains open.

also, from Iorio slides ON THE ANOMALOUS INCREASE OF THE ECCENTRICITY OF THE LUNAR ORBIT: SEARCH FOR POSSIBLE EXPLANATIONS , 2011, he try to offer: A VIABLE, empirical EXPLANATION

Let us assume that there is a small radial extra-acceleration of the form...

This procedure is called 'data fit' and obviously it is not an EXPLANATION at all.

I based my other answer on the decreasing LOD FACT, and all other answers are saying the contrary.

With this anser I make notice to the fact that an anomaly is present and that the present physics is unable to model it.

Again I point to a MODEL where the reported anomaly is not present because data is along with theory (eq 35 and 36).

I'm expecting a reception to this answer in line with the reception to the other answer.

May be the case that some doubt in your minds can rise the need to read 'out-of-the-box' and try to see if the Sun-Earth anomaly (AU increase) or the Pioneer anomaly can be explained by this model.

When we have the chance to make measures with more precision we have to report an anomaly.

A bunch of anomalies is a call for a new model.

I'm expecting that someday, somebody, will read that paper. It is a cosmological model that do not need DM, DE, Cosmological Constant, it goes well with GR, and agrees with data both at local scale and cosmological scale.