Armstrong: 1992
First Union Grand Prix
GP Sanson
Longsjo Classic (1 stage win)
Thrift Drug Classic
Vuelta La Riberia (overall, 3 stages)
Trittico Premondiale (1 stage win)
1993
World Cycling Championship - World Cycling Champion
CoreStates USPro Championship - United States National Cycling Champion
Tour de France (Stage 8)
Tour of America (overall)
Vuelta Ciclista a Galega
Trophee Laigueglia
Tour du Pont (1 stage win)
Tour of Sweden (1 stage win)
Kmart West Virginia Classic (overall, 2 stage wins)
Thrift Drug Classic
US Pro Championship (and the $1,000,000 triple crowm)
1994
Thrift Drug Classic
Tour du Pont (1 stage win)
1995
Tour de France (Stage 18)
Clasica San Sebastian
Paris-Nice (Stage 5)
Tour du Pont (overall, 3 stage wins)
Kmart West Virginia Classic (overall, 1 stage win)
Tour of America (overall)
1996
Tour du Pont (overall, 5 stage wins)
La Flèche Wallonne
1998
Rheinland-Pfalz Rundfahrt (overall)
Tour de Luxembourg (overall, 1 stage win)
Cascade Classic
1999
Tour de France (overall, 4 stage wins)
Critérium du Dauphiné Libéré (ITT) (Prologue)
Route du Sud (Stage 4)
Circuit de la Sarthe (ITT) (Stage 4)
2000
Tour de France (overall, 1 stage win)
GP des Nations
GP Eddy Merckx
Critérium du Dauphiné Libéré (ITT) (Stage 3)
Bronze medal in the 2000 Summer Olympics Individual Time Trial, Men
2001
Tour de France (overall, 4 stage wins)
Tour de Suisse (overall, 2 stage wins)
2002
Tour de France (overall, 4 stage wins)
Critérium du Dauphiné Libéré (Stage 6)
GP du Midi-Libre
2003
Tour de France (overall, 1 stage win, Team Time Trial)
Critérium du Dauphiné Libéré (overall, Stage 3 ITT)
2004
Tour de France (overall, 5 stage wins, Team Time Trial)
Tour de Georgia (overall, 2 stage wins)
Tour du Languedoc-Roussillon (Stage 5)
Volta ao Algarve (ITT) (Stage 4)
2005
Tour de France (overall, 2 stage wins, Team Time Trial, Individual Time Trial)
Lemond:
1983 World Pro Road Race
Dauphiné - Libéré
Critérium des As
Super Prestige Pernod Trophy
1985 1 stage, Tour de France
1986 Tour de France
1 stage, Tour de France
1 stage, Giro d'Italia
Points competition, Tour of Switzerland
1989 Tour de France
3 stages, Tour de France
World Pro Road Race
1990 Tour de France
The only thing Lemond has on Armstrong is 2 World Champioships to 1 for Armstrong, but Armstrong has 2 classics to zero for Lemond, so I think the all arounder argument fails.