Q: How to Install Safari 5.1.9 on Lion or Mountain Lion

You can't, it's for Snow Leo only (unless you make a virtual machine & install OS X 10.6.8 - but what is it you want to achieve  ?

I see now, but  don't think you'll find any practical way to do that, although a few safari extensions exist to add an rss button which can manage & open them in google reader or other apps.

There's a difference - at very least insofar as the supporting system frameworks are altered & in somewhat different places in Lion+ vs Snow.

Have a look with Pacifist & see if you can pull a Multi-Safari on it

If you do  - backup bookmarks/history etc first (as a minimum). I've mostly (a few years ago) found multi-safari very handy, but occasionally inconsistent when two 'safaris' are open at once.

There is another way to do this on Lion (typing this from v5.1.9 on Lion) although in a bit of a roundabout way - v5.1.9 runs just fine on Lion, just like v5.1.7 does (Apple did not have 2 different versions of Safari v5.1.7 for Snow Leopard and Lion - they were the same Safari package and it appears that v5.1.9 is just a small update to v5.1.7). 

You need access to a machine that has Snow Leopard and v5.1.9 on it.  Then copy the v5.1.9 application to a thumbdrive etc. to transport it to your Lion machine.  On your Lion machine make a new directory in the Applications directory (you could call it "Old Safari v519") and then copy your v5.1.9 (from snow leopard) into the new directory.  If you have v5.1.7 I'd keep that just in case v5.1.9 turns out to have any issues.

Always just run one Safari at a time (you don't want corruption with two versions of Safari trying to access and update the same support files at the same time - but v5.1.9 should run fine from its new directory (mine does).  I've noticed that if I've run v6 it wipes out the Top Sites view alert when sites have updated their RSS (you have to run v5.1.7 or .9 a couple of times for it to establish itself again).

I have Lion, but wanted to let Safari update in the 6.x updates so I'd have the latest security updates (I keep thinking I'm going to switch over to it but always come back), but didn't want to loose v5.1.7.  So, before I let the 6.x updates happen I copied the Safari (v5.1.7) application from the Applications directory and (made a new directory in Applications directory "old Safari" and pasted a copy of the v5.1.7 in there).  This way v5.1.7 runs fine and I've let Safari keep getting 6.x updates (although I can never get used to not having RSS in there).

I'm glad that it works in Lion

I tested in Mountain Lion 10.8.4, and Safari 5.1.9 doesn't open a window, & crashes if a site is picked from the bookmarks menu, Same in a new user account. I don't have Lion currently to check.