lake_model_intro, time_series_with_matrices, long_run_growth: four small fixes #862

Four small things found while these lectures were reviewed on their way into the shared lecture pool (QuantEcon/lectures#42). None is urgent. Line numbers are at 530ede2.

• lectures/lake_model_intro.md, line 96: $(u_0, e_o)$ should read $(u_0, e_0)$.
• lectures/lake_model_intro.md, plot_time_paths (line 291): the T parameter is never used, because the loop calls lm.simulate_path(x0=x) without it (line 338), so plot_time_paths(lm, T=...) changes nothing. The closing if ax is None: plt.show() (lines 359–360) never runs either, because ax was already replaced by new axes when it was None (lines 314–315). The figure still appears in a notebook, so only the guard is dead.
• lectures/time_series_with_matrices.md, the # Plot mean cell (line 467): each pass of for i in range(N) draws a fresh sample of N paths with series_process.sample_y(N, rng=rng) (line 472) and plots only its i-th row, so plotting 100 paths simulates 10,000, and μ_y is replotted on every pass. Drawing one sample before the loop and plotting the mean once gives the same picture. Separately, sample_y (line 437) could build ys as (b + us) @ A_inv.T rather than stacking one product per row.
• lectures/long_run_growth.md, the color_mapping cell (line 144): country_names = data['countrycode'] holds one entry per row of the data, not per country, so cm.tab20(np.linspace(0, 0.95, len(country_names))) (line 147) spaces the colours over every row, and the dictionary keeps the colour of each code's last row. The colours then depend on how many rows each country has. data['countrycode'].unique() gives one evenly spaced colour per country.

The same review also questioned r(A) = 1 + g at lake_model_intro.md line 272, but that is exact as written: every column of A sums to 1 + g.

When these land here, the pool picks them up through its nightly refresh.