Creating graph coordinate in LyX

marmot already gave you a code sample in his comment, but since you're using LyX maybe you need to know how to insert it in it.

Open your document and choose Document --> Settings --> LaTeX preamble and add

usepackage{tikz}
usetikzlibrary{arrows.meta}
usetikzlibrary{intersections, positioning}

and click on OK.

Then choose Insert --> TeX code (or click on Ctrl+L) and insert this code where the cursor is:

begin{tikzpicture}[>=Stealth] 
draw[->] (-0.5,0) -- (5,0) node[right]{$Q_x$}; 
draw[->] (0,-0.5) -- (0,5) node[above]{$P_x$}; 
draw[name path=firstdemand] (.5,4.5) parabola[bend at end] (4,.5) node[above left=7pt and 44pt] {$D(overline{P}_y,overline{T},I_0)$};
draw[name path=demand] (1.5,4.5) parabola[bend at end] (5,1) node[above right=14pt and -34pt] {$D(overline{P}_y,overline{T},I_1>I_0)$};
path[name path=line] (0,3) -- (4,3);
path [name intersections={of=demand and line,by=mypoint}];
draw[dashed] (-.3,3) node[left] {$P_0$} -- (mypoint);
path[name path=lowline] (0,2.5) -- (4,2.5);
path [name intersections={of=firstdemand and lowline,by=mylowpoint}];
draw[thick, ->] (mylowpoint) -- ++(.7,0);
end{tikzpicture}

(my code is a little different from marmot's one).

Then click on View, and you'll get this result: