Expose modes/tools as MCP server (lex-mcp run_http)

[alpibrupa]

Goal

Expose lex-code's modes/tools as an MCP server via lex-mcp run_http, so Claude Code / Cursor / any MCP host can drive lex-code natively (alongside the existing A2A + ACP transports).

Why

lex-code already defines rich AgentDefs (build/plan/explore/refactor/spec/test/review/multi) with a deep toolset. It's pure Pattern A — wrapping with lex-mcp run_http turns it into an IDE-consumable MCP server for ~free.

Scope

• Mount each mode (or a mode-selecting tool) over MCP HTTP using lex-mcp run_http.
• Keep A2A + ACP working; share the dispatch path (see lex-agent dual-mount helper).
• Decide tool granularity: one tool per mode vs. exposing the underlying tool set.
• Smoke test from an MCP host (e.g. Claude Code) end to end.

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Context: Part of the fleet-wide "define a capability once, expose it as A2A + MCP + ACLI CLI" effort. Adapters available: lex-agent (A2A), lex-mcp + new run_http (MCP), acli/acli-mcp (CLI→MCP). Reference implementation: elumobility/elu-cli (ACLI CLI) + alpibrusl/acli-mcp (bridge).