GDAL runs on most platforms, including Windows, so I'm not sure where you get the idea it only runs on Macs! The easiest way of getting installed on your machine is to download OSGeo4W, which is an installer for all manner of desktop GIS goodness, from which you can just choose GDAL/OGR.
Once you've done that, you can use the command line tool gdalwarp to reproject the images:
gdalwarp -t_srs EPSG:3857 -s_srs EPSG:9802 -r cubic -co "TILED=YES" input1.tif input2.tif ... input30.tif output.tif
Where EPSG:3857 is shorthand for the "Web Mercator" projection (thanks Sean!), and EPSG:9802 is the shorthand for the Lambert projection. You may need to use a different sampling algorithm instead of cubic, it depends on the sort of data you've got, and how it looks when it is warped. Specifying all the source images in one command line will avoid unsightly seams between the original images. the "TILED=YES" is sensible for almost any geo rasters to speed up access and display. See here for explanation of the parameters.
To split the image into tiles, you can use gdal2tiles.py (which you'll need to install Python, but that can be done with the OSGeo4W installer).
Addendum
It ocurred to me last night that you would need to specify the two lines of parallel and the central meridian of your source images on the command line, just using EPSG:9802 won't cut the mustard if that metadata isn't already in the source images. If that is the case, you'll need to change the -s_srs parameter to something like this:
-s_srs "+proj=lcc +lon_0=110 +lat_1=25 +lat_2=47 +datum=WGS84"
Where +lon_0 is the longitude of the central meridian, +lat_1 is the upper standard parallel, and +lat_2 is the lower standard parallel. If the images you're warping are of the same series, these values are likely to be the same for each image, but it is worth checking them first.
If you're unsure about how these projections work, you could do worse than looking here for an explanation.
A good point made by Rene W.
Here is the answer:
add +no_defs to your first example in order to avoid unwanted default values
about this part: +a=6367470 +b=6367470 +ellps=sphere +datum=WGS84
+datum=WGS84 is a shorthand for: +ellps=WGS84 +towgs84=0,0,0.
You already have +ellps=sphere. Your reference surface cannot be a shpere
and the WGS84 ellipsoid at the same time. As you already have +a=6367470
and +b=6367470, you should drop both +ellps=sphere and +datum=WGS84`
in case of doubts, use cs2cs -v for more info about which parameters
are actually takes, and which are ignored
Hermann
and
The default values of lat_1 and lat_2 are 33 and 45, so in your first
example you had +lat_1=46.244 +lat_2=45 which is not what you intended.
The second example does what you wanted.
Charles
Best Answer
The latitude of origin parameter is not a standard parallel. In a two-standard-parallel case of Lambert conformal conic, it is used to identify the origin of the northing / Y-coordinates only.
In the scale factor version of Lambert conformal conic, you specify the latitude of origin (or sometimes latitude of center) plus the scale factor. Mathematically, the scale factor, if less than 1, means that there are two implicit standard parallels, not quite symmetric around the latitude of origin.
For this second case, I have not seen a useful approximation for setting the scale factor parameter. I think you would need to find a program that reports the point linear scale factor (like the Tissot Indicatrix values). Set up the custom Lambert conic coordinate reference system, and then project some points to and see what is reported.
Or you could write your own program, that given the defining parameters, what are the implicit standard parallels?
I wrote an program to do so using John P. Snyder's Map Projections:A Working Manual several years ago. You'll want to look at book pages 107-8. On 108, he mentions how one equation is indeterminate if standard parallel 1 == standard parallel 2. My program is quite stupid, it just calculates a bunch of 'k' (scale factor at point) values given inputs ranges and I repeat the program, narrowing down the range until I get k=1 for one of the implicit standard parallels.