Can there be a context free language that is not recognizable by a PEG?
I see two flaws in this proof sketch, one related to CFLs vs CFGs, and another related to nested quantifiers and running time as a function of multiple parameters.

Any time you have a high-level proof strategy that seems to lead to surprising results, it is a good idea to check it carefully by expanding each step to obtain a detailed proof.  Expand each claim with a precise statement, by applying the definition or the exact theorem in the literature, and verify carefully that they match up.  This is particularly important when dealing with lower bounds, as they tend to introduce nested quantifiers that can lead your intuition astray when thinking only at a high level.

Flaw #1: CFLs vs CFGs

The proof seems to conflate context-free languages (CFLs) with context-free grammars (CFGs).  However, there can be multiple CFGs that all generate the same CFL.  At best, your proof strategy shows that there exists a CFG $G$ that can't be parsed by a PEG parser.  But that's not surprising; we already know that PEG parsers can only parse CFGs that are in the PEG format.  We cannot  conclude anything about the corresponding CFL $L(G)$; for all we know, there might exist some other grammar $G'$ that is a PEG grammar and that yields the same language, i.e., $L(G)=L(G')$.  Your proof doesn't rule that out, so it does not prove that the CFL it constructs can't be parsed by a PEG parser.

A concrete example of this is given at https://en.wikipedia.org/wiki/Parsing_expression_grammar#Expressive_power, which shows a simple CFG that cannot be parsed by a PEG parser, but where there exists another CFG for the same language that can be parsed by a PEG parser.

Flaw #2: Multiple parameters

It's important to expand out the statement of what is meant by these lower bounds.  The lower bound on matrix multiplication means that, for each matrix multiplication algorithm, there exists an infinite family $(A_1,B_1),(A_2,B_2),\cdots$ of matrices such that $A_n,B_n$ are $n\times n$ matrices, and multiplying $A_n \times B_n$ using this algorithm takes $\Omega(n^2)$ time.

Lee's reduction describes how to construct a matrix multiplication algorithm from any context-free parser.  If we now apply Lee's reduction to the matrix multiplication algorithm obtained from a PEG parser, we obtain an infinite family $(G_1,w_1),(G_2,w_2),\cdots$ of CFGs and inputs such that parsing them takes a long time.  You'll need to dive into the details of Lee's reduction to determine the sizes of the $G_n,w_n$.  Based on a quick look, it looks to me like the size of $G_n$ is $\Theta(n^2)$ and the size of $w_n$ is $\Theta(n^{1/3})$, but I'm not sure whether that's correct; you'd need to figure that out.

Next, you'd need to figure out the running time of a PEG parser, as a function of both the size $g$ of the grammar and the size $n$ of the input string.  Standard references state the running time of a packrat parser for a PEG grammar as $O(n)$, but they don't describe the dependence on $g$; is it $O(gn)$? $O(g^2n)$? something else?  You'd need to figure that out, and then apply it to the family above, to determine what the asymptotic running time of this parser is on the family $L_n,w_n$, and thus what the running time of this matrix multiplication algorithm is on the family $A_n,B_n$, to determine whether it contradicts the $\Omega(n^2)$ lower bound.

For instance, if the running time of a PEG parser is $O(gn)$, then Lee's reduction yields a matrix multiplication algorithm that takes $O(n^{2.333\ldots})$ time on the family $A_n,B_n$, which does not contradict the known lower bound.

Notice how Lee's result does not provide a single context-free grammar or context-free language where parsing is slow; it provides an infinite family of pairs of languages and inputs (which was not considered in your proof strategy).  Also note the importance of getting the nested quantifiers right, and of capturing how the running time of a parser depends on both the size of the input and on the size of the grammar (which was not considered in your proof strategy).  Hopefully this highlights how a strategy that sounds good can run into difficulties when one tries to apply it in detail; and one must check those details before assuming the strategy will work out.