The following steps will help build new regex messages and hopefully understand capture groups which make this work.

Open https://regex101.com

Paste the following log entry into the "TEST STRING" box.
(TestServer - Valguero_P) (1135239186:Lethal Tribe) Day 115, 16:06: Lethal claimed 'Baby Lethal - Lvl 436 (Sabertooth)'!

Your regex string will always begin with the following
^(.*:)\s
The above small amount of text should highlight GREEN and on the right you should see "Group 1." with the text it found.
Now we just need to add additional regex to build the additonal capture groups that we need to reformat the message as we want.

Next we want to capture my name "Lethal"
(\w+)\s
You should see "Lethal" turn pink/red and show as "Group 2." on the right with "Lethal" shown as the detected text.
The (\w+) captures the word "Lethal" and the \s represents a space but you can also just use a space instead if you prefer.

Next we need to put the action so it knows we are matching on the proper text.
We don't need to capture this text though so we won't be using any parenthesis.
claimed\s
The text will be blue meaning its part of the full match group.

Next we want to grab the dino the actiton was taken on.
('.*')
This basically says grab everything between the apostrophe's and assign it to a capture group and in this case "Group 3.".

Last up is the puncuation to end the full match needed for this to work.
!$
This will tell the regex the very last thing it should see is an exclamation mark. $ means end of the text which is our log entry.

When we put all these pieces together it will look like this (https://regex101.com/r/QkSR36/1)
^(.*:)\s(\w+)\sclaimed\s('.*')!$

Now that we have our regex built we need to put it in a form that is JSON friendly.
Using https://www.freeformatter.com/json-escape.html paste in the regex built above into this tool and click "ESCAPE"
It should give you an new box called "Escaped string:" and contain the following escaped regex
^(.*:)\\s(\\w+)\\sclaimed\\s('.*')!$

Once you have this you can move to adding this to the TribeLogRelay config.json file.
You need to wrap the escaped regex in quotations like this and buld the output format to the right of it.
"^(.*:)\\s(\\w+)\\sclaimed\\s('.*')!$":"$0"

Now we are back to looking at capture groups.
$0 = Full match "(TestServer - Valguero_P) (1135239186:Lethal Tribe) Day 115, 16:06: Lethal claimed 'Baby Lethal - Lvl 436 (Sabertooth)'!"
$1 = "(TestServer - Valguero_P) (1135239186:Lethal Tribe) Day 115, 16:06:"
$2 = "Lethal"
$3 = "'Baby Lethal - Lvl 436 (Sabertooth)'"

With this information we can now craft how we want the output to look.
"$1 $2 claimed $3!" is the same as just using $0 I built the exact same output using the capture groups.
"$1 $3 was claimed by $2!" will read "(TestServer - Valguero_P) (1135239186:Lethal Tribe) Day 115, 16:06: 'Baby Lethal - Lvl 436 (Sabertooth)' was claimed by Lethal!"

We will use the last one to refomat the text so the entry in the config.json would look like so
"^(.*:)\\s(\\w+)\\sclaimed\\s('.*')!$":"$1 $3 was claimed by $2!"